Complex đ | CompData | 3350 mathmath: ArithmeticFunction.vonMangoldt.residueClass_eq, Complex.norm_conj, Polynomial.logMahlerMeasure_one, CuspFormClass.qExpansion_isBigO, HurwitzZeta.hasSum_int_hurwitzZetaOdd, ModularForm.coe_mul, HurwitzZeta.jacobiThetaâ''_neg_left, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Complex.cos_sub_pi, Real.hasDerivAt_fourier, CStarAlgebra.preimage_inr_Icc_zero_one, WeakFEPair.differentiableAt_Î, NumberField.basisMatrix_eq_embeddingsMatrixReindex, TemperedDistribution.lineDerivOpCLM_eq, Real.circleAverage_map_add_const, Complex.log_one, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, Complex.log_conj_eq_ite, Polynomial.Chebyshev.S_two_mul_complex_cos, Complex.verticalSegment_eq, MeasureTheory.Lp.toTemperedDistributionCLM_apply, RCLike.sqrt_eq_ite, Complex.im_qsmul, Complex.cpow_intCast, UpperHalfPlane.mdifferentiable_num, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, Complex.cos_eq_tsum, ModularForm.mul_slash_SL2, isConformalMap_conj, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, NumberField.InfinitePlace.isNontrivial, HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_div, NumberField.InfinitePlace.eq_iff_isEquiv, Polynomial.mahlerMeasure_const, Polynomial.mahlerMeasure_def_of_ne_zero, EulerSine.integral_cos_mul_cos_pow, continuousAt_const_cpow, Complex.mul_im, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, Complex.UnitDisc.coe_eq_zero, Complex.ofNat_log, Complex.differentiableAt_sin, Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero, Complex.log_I, Complex.norm_circleTransformBoundingFunction_le, Complex.one_add_tan_sq_mul_cos_sq_eq_one, ModularForm.smul_slash, jacobiThetaâ_conj, Complex.re_mul_ofReal, GaussianInt.toComplex_mul, Complex.div_ofReal_re, ProbabilityTheory.isGaussian_iff_gaussian_charFun, Complex.isOpen_re_lt_EReal, Complex.nnnorm_exp_I_mul_ofReal, LSeries.abscissaOfAbsConv_one, Complex.log_neg_one, Measurable.complex_ofReal, differentiable_const_cpow_of_neZero, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, Complex.restrictScalars_one_smulRight', Complex.sin_eq_zero_iff_cos_eq, completedZeta_eq_tsum_of_one_lt_re, Complex.sinh_conj, Complex.continuousOn_exp, Complex.coe_realPart, Complex.log_re, IsSelfAdjoint.quasispectrumRestricts, NumberField.mixedEmbedding.logMap_one, EisensteinSeries.linear_inv_isBigO_left, CuspFormClass.holo, IsStarNormal.spectralRadius_eq_nnnorm, NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm, Complex.UnitDisc.normSq_lt_one, SlashInvariantForm.coe_prodEqualWeights, SchwartzMap.integral_sesq_fourier_fourier, PeriodPair.G_eq_zero_of_odd, HurwitzZeta.differentiableAt_hurwitzZeta_sub_one_div, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, ModularFormClass.differentiableAt_comp_ofComplex, MeasureTheory.charFun_eq_fourierIntegral', PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, Real.hasFDerivAt_fourierChar_neg_bilinear_left, Complex.cos_three_mul, Complex.linearEquiv_det_conjLIE, Ideal.toCharacterSpace_apply_eq_zero_of_mem, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, EisensteinSeries.hasSum_e2Summand_symmetricIcc, Complex.normSq_pos, Complex.mk_eq_add_mul_I, ValueDistribution.proximity_zero, HurwitzZeta.differentiableAt_hurwitzZetaEven, Complex.reProdIm_nonempty, UnitAddTorus.coe_mFourierBasis, Complex.Gammaâ_def, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, Complex.lim_conj, ModularFormClass.hasFPowerSeries_cuspFunction, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, CFC.monotoneOn_one_sub_one_add_inv, NumberField.canonicalEmbedding.mem_span_latticeBasis, Real.fderiv_fourierIntegral, Complex.iteratedDeriv_even_cosh, ModularFormClass.qExpansionFormalMultilinearSeries_radius, Complex.sin_pi_div_two_sub, PeriodPair.hasSumLocallyUniformly_weierstrassP, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, AlgHomClass.instStarHomClass, NonUnitalCStarAlgebra.toStarModule, Complex.circleTransformDeriv_eq, Real.circleAverage_sub, LSeries.term_sum, HurwitzZeta.hasSum_int_cosKernelâ, Complex.isOpenMap_im, Complex.exp_eq_exp_iff_exists_int, CuspForm.toFun_eq_coe, Int.cast_complex_isTheta_cast_real, NumberField.mixedEmbedding.convexBodyLT'_mem, HurwitzZeta.hasSum_int_hurwitzZetaEven, NumberField.InfinitePlace.comap_mk, Complex.ofRealCLM_coe, Complex.kahler, Complex.norm_polarCoord_symm, Complex.norm_sub_eq, ProbabilityTheory.eqOn_complexMGF_of_mgf', SchwartzMap.inner_fourier_toL2_eq, Complex.areaForm, Complex.re_eq_add_conj, SchwartzMap.toLp_fourierTransformInv_eq, CliffordAlgebraComplex.ofComplex_conj, finrank_real_complex_fact', PeriodPair.deriv_weierstrassP, Complex.instIsComplete, GaussianInt.intCast_im, CStarModule.innerââ_apply, PeriodPair.coeff_weierstrassPExceptSeries, Complex.ofReal_eq_one, summable_riemannZetaSummand, Complex.normSq_natCast, Real.fourierIntegralInv_eq', PositiveLinearMap.apply_le_of_isSelfAdjoint, Complex.analyticAt_cosh, qExpansion_eq_zero_iff, SlashInvariantForm.slash_action_eq', Complex.comap_exp_cobounded, Complex.cos_mul_I, ModularForm.mul_slash, ZMod.LFunction_modOne_eq, Complex.meromorphic_digamma, ZMod.LFunction_stdAddChar_eq_expZeta, Complex.norm_le_abs_re_add_abs_im, Complex.cos_sub_sin_I, Circle.exp_arg, Complex.tan_nat_mul_pi_sub, Circle.injective_arg, norm_jacobiThetaâ_term_le, GaussianInt.toComplex_def', CFC.monotone_nnrpow, MeasureTheory.charFunDual_apply, DirichletCharacter.LSeries_eulerProduct_tprod, Polynomial.Chebyshev.complex_ofReal_eval_S, PeriodPair.iteratedDeriv_weierstrassPExcept_self, Complex.mem_integerComplement_iff, qExpansionRingHom_apply, LSeries.term_convolution', Complex.ofRealLI_apply, CuspFormClass.zero_at_infty_comp_ofComplex, Complex.GammaIntegral_eq_mellin, PeriodPair.derivWeierstrassPExcept_sub, Complex.isTheta_cpow_rpow, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries, isLittleO_exp_neg_mul_sq_cocompact, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, norm_jacobiThetaâ_term_fderiv_ge, UpperHalfPlane.normSq_pos, NumberField.canonicalEmbedding.latticeBasis_apply, Complex.integral_comp_pi_polarCoord_symm, CFC.tendsto_cfc_rpow_sub_one_log, Complex.Gamma_neg_nat_eq_zero, HurwitzZeta.cosZeta_two_mul_nat', Complex.norm_mul_self_eq_normSq, Complex.Gamma_nat_eq_factorial, Complex.real_smul, NumberField.InfinitePlace.le_iff_le, Complex.real_algHom_eq_id_or_conj, summableLocallyUniformlyOn_iteratedDerivWithin_cexp, NumberField.norm_norm_le_norm_mul_house_pow, countingFunction_finsum_eq_finsum_add, Complex.add_im, UpperHalfPlane.image_coe_sphere, realPart_ofReal, Complex.digamma_apply_add_one, Complex.isCoveringMap_exp, Complex.cos_eq_one_iff, ModularForm.constâ_apply, PeriodPair.Ďâ_div_two_notMem_lattice, Complex.reProdIm_subset_iff', Complex.equivRealProdAddHom_symm_apply, range_circleMap, NumberField.mixedEmbedding.convexBodySumFun_add_le, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, UpperHalfPlane.re_smul, span_fourier_closure_eq_top, Real.fourierIntegral_eq, ModularForm.eta_q_eq_pow, Complex.GammaSeq_tendsto_Gamma, PeriodPair.basis_one, Complex.inv_I, OnePoint.isBoundedAt_iff_exists_SL2Z, CStarAlgebra.inr_mem_Icc_iff_norm_le, HurwitzZeta.sinZeta_neg_two_mul_nat_sub_one, Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, Complex.natCast_re, NumberField.isInfinitePlace_iff, one_add_cpow_hasFPowerSeriesAt_zero, Complex.arg_neg_I, circleIntegrable_iff, DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontriv, UpperHalfPlane.int_div_mem_integerComplement, Complex.conj_inv, Complex.tsum_exp_neg_mul_int_sq, not_integrableOn_Ioi_cpow, Real.fderiv_fourierChar_neg_bilinear_right_apply, NumberField.InfinitePlace.isometry_embedding, BoundedContinuousFunction.char_neg, UpperHalfPlane.isOpenEmbedding_coe, Real.fourier_continuousLinearMap_apply, ZMod.dft_even_iff, Unitization.real_cfcâ_eq_cfc_inr, Complex.exp_add_mul_I, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex, ZMod.invDFT_apply, Complex.range_cos, NumberField.mixedEmbedding.normAtAllPlaces_apply, imaginaryPart_I_smul, Quaternion.coeComplex_mul, Complex.uniformlyContinuous_im, NumberField.mem_maximalRealSubfield_iff, BoundedContinuousFunction.char_zero_eq_one, SchwartzMap.lineDerivOp_fourier_eq, Polynomial.logMahlerMeasure_C_mul, Complex.arg_cos_add_sin_mul_I_coe_angle, Complex.analyticOn_sin, Complex.not_le_iff, DirichletCharacter.LSeries_modOne_eq, EisensteinSeries.summand_bound_of_mem_verticalStrip, Complex.measurable_arg, Complex.star_def, Complex.tan_pi_sub, SchwartzMap.integral_bilin_fourierInv_eq, Function.Periodic.cuspFunction_zero_eq_limUnder_nhds_ne, LSeries_injOn, circleMap_neg_pi_div_two, UpperHalfPlane.comp_ofComplex_of_im_pos, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, GaussianFourier.integral_cexp_neg_mul_sq_norm, AddChar.doubleDualEmb_injective, Complex.div_ofNat_im, Complex.arg_div_self, LSeries_eventually_eq_zero_iff', NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, HurwitzZeta.jacobiThetaâ''_add_left, Complex.continuousOn_arg, Complex.lipschitz_equivRealProd, Function.Periodic.norm_qParam_le_of_one_half_le_im, UpperHalfPlane.dist_le_iff_dist_coe_center_le, Complex.angle_exp_one, Complex.angle_div_right_eq_angle_mul_left, hasSum_one_div_nat_pow_mul_fourier, NumberField.mixedEmbedding.norm_unit_smul, two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even, Complex.arg_of_re_nonneg, Complex.nndist_self_conj, Complex.betaIntegral_scaled, Complex.cos_eq_zero_iff, Complex.cos_sub, NumberField.mixedEmbedding.norm_eq_norm, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, fourierCoeffOn.const_mul, Complex.cos_antiperiodic, Complex.cos_add_nat_mul_two_pi, NumberField.mixedEmbedding.norm_le_convexBodySumFun, SlashInvariantForm.quotientFunc_mk, DirichletCharacter.LSeriesSummable_of_one_lt_re, mellin_div_const, Complex.UnitDisc.instSMulCommClass_closedBall_circle, TemperedDistribution.lineDerivOp_fourier_eq, Complex.frontier_setOf_re_le, MeasureTheory.charFun_neg, WeakFEPair.symm_Îâ_eq, ModularForm.SL_slash, Complex.mul_re, VonNeumannAlgebra.ext_iff, Complex.ofRealCLM_norm, Complex.UnitDisc.instSMulCommClass_closedBall_left, Complex.instIsScalarTowerOfReal, Complex.reLm_coe, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, StarAlgebra.elemental.characterSpaceToSpectrum_coe, HurwitzZeta.cosZeta_two_mul_nat, rotation_injective, Bornology.IsBounded.reProdIm, Circle.ofConjDivSelf_coe, NumberField.mixedEmbedding.mem_idealLattice, Polynomial.one_le_prod_max_one_norm_roots, Complex.re_balance, UpperHalfPlane.im_smul_eq_div_normSq, Complex.borelSpace, Complex.norm_eq_one_iff', NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, Complex.sin_eq_neg_one_iff, Complex.equivRealProd_apply, UpperHalfPlane.specialLinearGroup_apply, SlashInvariantForm.coe_constâ, Complex.iteratedDeriv_odd_sinh, Complex.cpow_mul_ofReal_nonneg, riemannZeta_two, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, Complex.convexHull_reProdIm, SlashInvariantForm.smul_applyâ, Complex.conjLIE_apply, Complex.hasStrictDerivAt_tan, Circle.starRingEnd_addChar, HurwitzZeta.cosZeta_neg_two_mul_nat_add_one, Complex.closure_preimage_im, fourierIntegral_gaussian_innerProductSpace', UpperHalfPlane.canLift, Complex.cosh_conj, Complex.range_sin, Complex.sqrt_I, fourier_gaussian_pi', MeasureTheory.charFun_eq_fourierIntegral, LSeriesSummable.smul, Complex.oangle, NumberField.InfiniteAdeleRing.algebraMap_apply, Complex.IsExpCmpFilter.isBigO_im_pow_re, UnitAddTorus.mFourierSubalgebra_coe, Complex.range_re, CStarModule.normedSpaceCore, iteratedDerivWithin_tsum_cexp_eq, Complex.continuousWithinAt_log_of_re_neg_of_im_zero, UpperHalfPlane.Ď_sq, PeriodPair.iteratedDeriv_derivWeierstrassPExcept_self, jacobiThetaâ_functional_equation, ZMod.dft_mul_const, Complex.continuous_sin, intervalIntegral.integral_ofReal, Complex.reProdIm_subset_iff, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, Complex.exp_eq_exp_â, Complex.cosh_three_mul, Complex.sin_int_mul_pi, Complex.im_expect, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept, norm_cexp_neg_mul_sq, PeriodPair.weierstrassP_coe, UpperHalfPlane.num_neg, ModularForm.coe_constâ, Polynomial.Chebyshev.complex_ofReal_eval_T, Complex.hasStrictFDerivAt_exp_real, Complex.sin_eq_zero_iff, UpperHalfPlane.moebius_im, ModularForm.prod_slash, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Complex.isQuotientCoveringMap_npow, WithCStarModule.prod_norm_sq, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, Complex.tan_pi_div_two_sub, CStarModule.innerSL_apply, DirichletCharacter.LSeries_twist_vonMangoldt_eq, Real.norm_exp_I_mul_ofReal_sub_one_le, Real.vector_fourierIntegral_eq_integral_exp_smul, HurwitzZeta.evenKernel_def, UnitAddTorus.mFourierSubalgebra_closure_eq_top, ModularGroup.one_lt_normSq_T_zpow_smul, Complex.Gamma_add_one, Real.fourier_real_eq_integral_exp_smul, Complex.cpow_neg_one, Complex.deriv_cos, Complex.instFiniteDimensionalReal, CStarAlgebra.span_nonneg_inter_unitBall, Complex.nnnorm_ratCast, Complex.not_differentiableAt_Gamma_neg_nat, AddCircle.homeomorphCircle'_symm_apply, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, Complex.normSq_ratCast, SlashInvariantForm.add_apply, torusIntegral_succ, MeasureTheory.Lp.instFourierInvSMul, CuspForm.zero_apply, DirichletCharacter.LFunction_eq_LSeries, HurwitzZeta.jacobiThetaâ'_functional_equation', Complex.norm_cos_add_sin_mul_I, HurwitzZeta.hurwitzZetaEven_def_of_ne_or_ne, Function.Periodic.norm_qParam_lt_iff, Complex.angle_mul_left, Complex.cos_pi_div_two, ModularForm.norm_eq_zero_iff, continuous_const_cpow, Complex.norm_pow, analyticOnNhd_circleMap, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, NumberField.mixedEmbedding.commMap_apply_of_isComplex, WithCStarModule.inner_def, Complex.arg_one, hasSum_nat_jacobiTheta, CircleIntegrable.const_smul, NumberField.InfinitePlace.Completion.norm_coe, Real.fourier_deriv, Complex.Gamma_one, differentiableOn_iteratedDerivWithin_cotTerm, circleMap_zero_inv, DirichletCharacter.norm_LSeries_product_ge_one, Complex.exp_add, PeriodPair.hasSum_derivWeierstrassPExcept, CliffordAlgebraComplex.ofComplex_toComplex, ArithmeticFunction.LSeries_zeta_mul_Lseries_moebius, rotation_apply, toMatrix_rotation, NumberField.mixedEmbedding.instNoAtomsMixedSpaceVolume, Complex.normSq_mk, GaussianInt.toComplex_defâ, Complex.digamma_one_half, ZMod.stdAddChar_coe, SlashInvariantFormClass.eq_cuspFunction, ValueDistribution.proximity_pow_zero, Complex.differentiableAt_GammaAux, Complex.toBasis_orthonormalBasisOneI, CliffordAlgebraComplex.toComplex_comp_ofComplex, gelfandStarTransform_naturality, ModularForm.prod_slash_sum_weights, Complex.isCauSeq_conj, gelfandStarTransform_apply_apply, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, Complex.instPathConnectedSpaceUnits, ZMod.completedLFunction_zero, GaussianInt.normSq_le_normSq_of_re_le_of_im_le, PeriodPair.weierstrassP_zero, EisensteinSeries.e2Summand_even, NumberField.mixedEmbedding.convexBodyLT_volume, ModularGroup.coe_apply_complex, Real.nnnorm_exp_I_mul_ofReal_sub_one_le, WeakFEPair.h_feq, ArithmeticFunction.abscissaOfAbsConv_zeta, integrableOn_Ioi_norm_cpow_of_lt, OnePoint.isBoundedAt_iff_forall_SL2Z, Complex.UnitDisc.coe_neg, Complex.integral_rpow_mul_exp_neg_rpow, Complex.continuousOn_cos, Complex.exp_def, Real.circleAverage_sum, Complex.arg_mul_eq_add_arg_iff, SchwartzMap.integral_fourierInv_smul_eq, SlashInvariantForm.quotientFunc_smul, Complex.sin_nat_mul_pi, Complex.tan_int_mul_pi, Complex.volume_sum_rpow_le, CircleIntegrable.neg, PeriodPair.analyticAt_weierstrassPExcept, summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm, SchwartzMap.inner_toL2_toL2_eq, Complex.isOpen_slitPlane, Complex.analyticWithinAt_cosh, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, jacobiThetaâ'_conj, MeasureTheory.SignedMeasure.toComplexMeasure_apply, ModularForm.tsum_logDeriv_eta_q, ModularForm.levelOne_neg_weight_rank_zero, EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear, ValueDistribution.proximity_coe_eq_proximity_sub_const_zero, Complex.coe_orthonormalBasisOneI, CStarMatrix.toCLM_injective, SlashInvariantForm.constâ_toFun, Complex.integral_circleTransform, StrongFEPair.differentiable_Î, Polynomial.toAddCircle_X_pow_eq_fourier, DirichletCharacter.LFunction_changeLevel, CuspFormClass.zero_at_cusps, Complex.cot_inv_eq_tan, SlashInvariantForm.one_coe_eq_one, HurwitzZeta.oddKernel_def', Complex.cos_conj, Complex.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, gelfandTransform_bijective, SchwartzMap.integral_bilin_fourierIntegral_eq, fourier_gaussian_innerProductSpace, Real.fourierIntegral_continuousMultilinearMap_apply, Complex.tan_nat_mul_pi, NumberField.mixedEmbedding.polarSpaceCoord_target, OnePoint.isZeroAt_iff_exists_SL2Z, circleMap_sub_center, SchwartzMap.toLp_fourierInv_eq, NumberField.mixedEmbedding.negAt_apply_snd, Complex.sinh_add_cosh, GaussianInt.toComplex_div_re, bernoulliFourierCoeff_zero, Complex.contDiff_cosh, Complex.isPrimitiveRoot_exp_rat, SlashInvariantForm.smul_apply, Complex.im_nnqsmul, VectorFourier.fourierPowSMulRight_eq_comp, SlashInvariantForm.coe_smulâ, Complex.analyticOn_cosh, Complex.measurableEquivPi_apply, Polynomial.cyclotomic.eval_apply_ofReal, EisensteinSeries.E2_slash_action, Complex.tendsto_exp_nhds_zero_iff, fourier_norm, Complex.uniformContinuous_im, Complex.mem_rootsOfUnity, MeasureTheory.charFun_apply, Complex.one_div_Gamma_eq_self_mul_one_div_Gamma_add_one, Complex.frontier_preimage_re, CuspForm.coe_trace, EisensteinSeries.e2Summand_summable, Complex.sin_int_mul_two_pi_sub, image_circleMap_Ioc, NumberField.mixedEmbedding.convexBodyLT_mem, NumberField.InfinitePlace.coe_apply, UpperHalfPlane.glPos_smul_def, Unitization.inr_le_iff, Complex.sub_im, Complex.cos_nat_mul_two_pi_sub_pi, NumberField.mixedEmbedding.convexBodySumFun_apply', NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, Complex.reCLM_nnnorm, Complex.nndist_of_im_eq, UpperHalfPlane.coe_pos_real_smul, Unitization.instStarOrderedRing, ModularGroup.coe_T_zpow_smul_eq, Complex.instContinuousStar, Function.HasTemperateGrowth.toTemperedDistribution_apply, NumberField.mixedEmbedding.convexBodySum_neg_mem, NumberField.mixedEmbedding.negAt_preimage, Complex.hasDerivAt_GammaIntegral, Complex.deriv_ofReal_cpow_const, UpperHalfPlane.comp_ofComplex, LSeries_iteratedDeriv, Complex.starConvex_ofReal_slitPlane, NumberField.ComplexEmbedding.conjugate_comp, ModularForm.coe_neg, CuspForm.coeHom_apply, Complex.analyticOnNhd_univ_iff_differentiable, SchwartzMap.integral_sesq_fourier_eq, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, Real.fderiv_fourier, MeasureTheory.charFunDual_pi', CStarMatrix.norm_def', NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Complex.two_sinh, HurwitzZeta.hasSum_nat_sinZeta, Complex.exp_zero, Complex.isometry_conj, Complex.exp_antiperiodic, EisensteinSeries.G2_slash_action, ArithmeticFunction.not_LSeriesSummable_moebius_at_one, SlashInvariantForm.const_toFun, NumberField.mixedEmbedding.normAtPlace_apply_of_isReal, MeasureTheory.charFun_apply_real, StrongFEPair.functional_equation, Complex.UnitDisc.coe_smul_circle, fourierCoeff_bernoulli_eq, Complex.exp_add_pi_mul_I, Complex.log_exp_eq_re_add_toIocMod, Complex.summable_conj, UpperHalfPlane.denom_cocycle_Ď, VectorFourier.fourierIntegral_continuousLinearMap_apply, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, circleMap_eq_circleMap_iff, Complex.analyticOn_sinh, Complex.log_inv_eq_ite, PeriodPair.latticeBasis_zero, circleIntegral.integral_sub_inv_smul_sub_smul, EulerSine.integral_cos_mul_cos_pow_aux, SchwartzMap.fourier_lineDerivOp_eq, Complex.equivRealProd_symm_apply, Complex.starConvex_one_slitPlane, Polynomial.logMahlerMeasure_mul_eq_add_logMahelerMeasure, TemperedDistribution.instLineDerivLeftSMulReal, LindemannWeierstrass.exp_polynomial_approx, Polynomial.Chebyshev.complex_ofReal_eval_C, CStarMatrix.inner_toCLM_conjTranspose_left, Complex.normSq_mul, UpperHalfPlane.re_add_im, Complex.interior_setOf_le_re, DirichletCharacter.mul_delta, Filter.tendsto_ofReal_iff, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, NumberField.ComplexEmbedding.Extension.not_isReal_of_not_isReal, TemperedDistribution.fourierInv_lineDerivOp_eq, Complex.mul_conj', UpperHalfPlane.mdifferentiable_inv_denom, RCLike.complexRingEquiv_apply, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, Real.fourier_iteratedFDeriv, Orientation.kahler_eq_zero_iff, AddChar.sum_apply_eq_ite, Complex.arg_cos_add_sin_mul_I, PositiveLinearMap.preGNS_norm_def, PositiveLinearMap.leftMulMapPreGNS_apply, Complex.cpow_ofNat_mul', ValueDistribution.proximity_inv, Complex.cos_eq_iff_quadratic, UpperHalfPlane.dist_eq_iff_eq_sinh, Complex.arg_of_re_neg_of_im_nonneg, LSeries.term_def, Complex.integral_comp_polarCoord_symm, Complex.uniformContinuous_re, riemannZeta_one_sub, Complex.liftAux_apply, SchwartzMap.integral_norm_sq_fourier, PeriodPair.Ďâ_div_two_notMem_lattice, Complex.reProdIm_eq_empty, PeriodPair.derivWeierstrassP_neg, UnitAddTorus.mFourierCoeff_toLp, NumberField.exists_conjugate_one_le_norm, NumberField.InfinitePlace.conjugate_embedding_injective, HurwitzZeta.differentiable_expZeta_of_ne_zero, Complex.ratCast_im, NumberField.InfinitePlace.norm_embedding_eq, PeriodPair.hasSum_derivWeierstrassP, Complex.sinh_three_mul, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, PeriodPair.compl_lattice_diff_singleton_mem_nhds, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, ext_inner_map, NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zero, integrableOn_Ioi_cpow_iff, mellin_hasDerivAt_of_isBigO_rpow, HurwitzZeta.differentiable_hurwitzZetaOdd, integral_exp_mul_complex_Ioi, setIntegral_Ioi_zero_cpow, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, LSeries_deriv_eqOn, GaussianInt.toComplex_injective, deriv_norm_ofReal_cpow, Complex.natCast_im, TemperedDistribution.instFourierAdd, HurwitzZeta.differentiable_hurwitzZeta_sub_hurwitzZeta, Complex.tan_eq_zero_iff', PeriodPair.hasSumLocallyUniformly_derivWeierstrassP, Complex.sameRay_of_arg_eq, HurwitzZeta.completedSinZeta_neg, SlashInvariantForm.coe_translate, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, Complex.cos_nat_mul_two_pi, Complex.ofReal_zpow, Complex.measurableEquivRealProd_apply, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, UpperHalfPlane.ofComplex_apply_of_im_nonpos, Complex.natCast_mul_natCast_cpow, Orientation.kahler_swap, Complex.exp_eq_exp_iff_exp_sub_eq_one, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, IsOpen.reProdIm, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, Complex.betaIntegral_eval_one_right, Complex.ofReal_cpow, SlashInvariantForm.ext_iff, Complex.frontier_setOf_im_lt, cauchyPowerSeries_apply, summable_eisSummand, Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasure, LSeries_analyticOnNhd, ModularFormClass.levelOne_neg_weight_eq_zero, ModularFormClass.continuous, norm_circleMap_zero, ContinuousLinearMap.instStarOrderedRing, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, IsSelfAdjoint.coe_mem_spectrum_complex, Complex.ofReal_mul', Complex.UnitDisc.coe_conj, contDiff_circleMap, Complex.exp_nsmul, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, Complex.betaIntegral_recurrence, NumberField.InfinitePlace.mkReal_coe, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, Complex.arg_of_im_pos, qExpansion_of_mul, Complex.sin_sub_nat_mul_two_pi, Complex.cosh_sq_sub_sinh_sq, Complex.tendsto_exp_comap_re_atTop, measurable_circleMap, convex_halfSpace_re_le, Complex.reCLM_coe, VectorFourier.hasFDerivAt_fourierIntegral, Complex.deriv_Gamma_add_one, HurwitzZeta.hurwitzZetaEven_apply_zero, CompletelyPositiveMap.instLinearMapClassComplex, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux', LSeriesHasSum.convolution, Complex.arg_neg_eq_arg_sub_pi_of_im_pos, Complex.ofReal_cpow_of_nonpos, Complex.continuous_re, Complex.sin_nat_mul_two_pi_sub, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, Complex.sin_two_mul, NumberField.InfinitePlace.smul_mk, orthonormal_fourier, VectorFourier.fourierIntegral_iteratedFDeriv, UpperHalfPlane.contMDiff_coe, jacobiThetaâ_neg_left, CuspForm.holo', integrableOn_Ioi_norm_cpow_iff, HurwitzZeta.expZeta_one_sub, Complex.analyticAt_sin, PeriodPair.mem_lattice, BoundedContinuousFunction.mem_charPoly, spectrum.gelfandTransform_eq, HurwitzZeta.cosZeta_apply_zero, ModularGroup.denom_apply, Orientation.kahler_comp_rightAngleRotation, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, BoundedContinuousFunction.charAlgHom_apply, Complex.norm_natCast, ArithmeticFunction.vonMangoldt.residueClass_apply, Complex.lift_apply, NumberField.ComplexEmbedding.involutive_conjugate, TemperedDistribution.delta_apply, MeasureTheory.memLp_haarAddCircle_iff, Circle.arg_eq_arg, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, NumberField.mixedEmbedding.convexBodySum_compact, Unitary.norm_sub_one_lt_two_iff, PeriodPair.weierstrassPExcept_neg, LSeries_sub, Complex.log_inv, fourierIntegral_gaussian_pi, ProbabilityTheory.complexMGF_mul_I, LSeries_neg, NumberField.Units.map_complexEmbedding_torsion, Real.circleAverage_eq_circleIntegral, Complex.norm_exp_I_mul_ofReal_sub_one, injOn_circleMap_of_abs_sub_le', integral_exp_mul_complex, CuspFormClass.petersson_bounded_left, MeasureTheory.charFunDual_prod, CStarAlgebra.span_nonneg, Complex.ofReal_comp_sub, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, Complex.arg_cos_add_sin_mul_I_sub, Complex.sub_re, Complex.sq_norm_sub_sq_re, Complex.comap_exp_nhds_zero, EisensteinSeries.G2_eq_tsum_symmetricIco, Complex.equivRealProdCLM_symm_apply, Complex.abs_re_eq_norm, TemperedDistribution.instContinuousFourier, Complex.cos_eq_tsum', mellinInv_eq_fourierIntegralInv, Complex.norm_add_eq, CStarModule.inner_smul_right_complex, DirichletCharacter.differentiableAt_LFunction, Complex.norm_cpow_of_ne_zero, NumberField.canonicalEmbedding.integralBasis_repr_apply, Complex.interior_preimage_re, Complex.continuous_cosh, fourier_one, Complex.natCast_log, MeasureTheory.charFun_eq_prod_iff, Complex.digamma_zero, Complex.cos_pi_sub, Complex.im_le_norm, Complex.norm_ofReal_cpow_eventually_eq_atTop, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, Complex.integral_exp_neg_rpow, Complex.mem_slitPlane_iff_arg, LSeries.term_sub, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, DirichletCharacter.LSeriesSummable_mul, Complex.norm_mul_cos_arg, Complex.sq_norm, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, Complex.measurable_re, ModularForm.coe_natCast, Complex.Gamma_conj, UpperHalfPlane.Ď_mul, PeriodPair.basis_zero, UpperHalfPlane.image_coe_ball, NumberField.ComplexEmbedding.IsConj.eq, Complex.exists_norm_eq_mul_self, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Complex.closure_setOf_lt_im, Real.Angle.coe_toCircle, Complex.integerComplement.add_coe_int_mem, tendsto_integral_exp_smul_cocompact, Complex.UnitDisc.coe_pow, Complex.hasDerivAt_Gammaâ_one, Complex.dist_self_conj, ProbabilityTheory.eqOn_complexMGF_of_mgf, hasSum_jacobiThetaâ_term, Complex.ofReal_neg, Complex.cpow_sub, hasFDerivAt_jacobiThetaâ_term, Complex.continuousAt_cpow_const_of_re_pos, Real.fourierIntegral_continuousLinearMap_apply, LSeries_deriv, Polynomial.logMahlerMeasure_X_sub_C, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, Complex.div_ofNat, UpperHalfPlane.contMDiff_inv_denom, ModularForm.coe_prodEqualWeights, gelfandStarTransform_symm_apply, NumberField.InfinitePlace.card_filter_mk_eq, Complex.smul_re, circleMap_pi_div_two, riemannZeta_four, Complex.uniformlyContinuous_re, Complex.map_exp_comap_re_atTop, Complex.cos_two_mul, Polynomial.mahlerMeasure_eq_zero_iff, Complex.orthonormalBasisOneI_repr_apply, EisensteinSeries.summable_norm_eisSummand, Quaternion.coeComplex_add, ZMod.dft_comp_unitMul, Complex.differentiable_exp, Complex.UnitDisc.isEmbedding_coe, HurwitzZeta.hasSum_nat_completedCosZeta, tendsto_sub_mul_tsum_nat_cpow, Polynomial.toAddCircle.integrable, Complex.ofNat_mem_slitPlane, fourier_zero, Complex.cos_sub_two_pi, Complex.normSq_I, Complex.partialGamma_add_one, Complex.sin_sub_two_pi, fourier_neg', CStarModule.inner_smul_left_complex, SchwartzMap.delta_apply, Complex.sin_sub_pi_div_two, DirichletCharacter.LSeries_changeLevel, SchwartzMap.norm_fourier_toL2_eq, norm_cauchyPowerSeries_le, Complex.tan_neg, Complex.re_comp_balance, Complex.cos_add_sin_mul_I_pow, mellinInv_eq_fourierInv, summable_jacobiThetaâ_term_fderiv_iff, Complex.norm_eq_one_iff, Complex.exp_ofReal_mul_I_re, fourier_gaussian_innerProductSpace', HurwitzZeta.hasSum_nat_hurwitzZetaEven, VectorFourier.fourierIntegral_const_smul, Complex.arg_mul_cos_add_sin_mul_I, LSeries.term_of_ne_zero, HurwitzZeta.hasSum_int_cosKernel, Real.fourier_real_eq, LSeries_smul, UpperHalfPlane.norm_Ď, Complex.cpow_eq_zero_iff, OnePoint.isZeroAt_infty_iff, Circle.smul_def, Complex.IsExpCmpFilter.isLittleO_exp_cpow, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, PeriodPair.isClosed_lattice, Complex.div_ratCast_re, integral_cpow, Complex.tanh_neg, IsSelfAdjoint.val_re_map_spectrum, realPart.norm_le, BoundedContinuousFunction.innerProbChar_zero, ProbabilityTheory.iteratedDeriv_complexMGF, Complex.tendsto_normSq_cocompact_atTop, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, NumberField.mixedEmbedding.convexBodySumFun_apply, Real.tendsto_integral_gaussian_smul', Real.hasFDerivAt_fourier, HurwitzZeta.hurwitzZeta_neg_nat, convex_halfSpace_im_gt, norm_jacobiThetaâ_term, EisensteinSeries.tendsto_zero_inv_linear_sub, Complex.exp_neg_pi_div_two_mul_I, GaussianFourier.integrable_cexp_neg_mul_sum_add, Complex.continuousOn_sin, tendsto_riemannZeta_sub_one_div, ZetaAsymptotics.tendsto_Gamma_term_aux, NumberField.InfinitePlace.Completion.locallyCompactSpace, Complex.exp_nsmul', Complex.polarCoord_apply, Real.fourierIntegral_convergent_iff', Complex.differentiable_iteratedDeriv_sin, AddChar.expect_apply_eq_zero_iff_ne_zero, Complex.normSq_add, Complex.hasStrictDerivAt_sinh, Complex.ofReal_balance, inner_map_polarization', EisensteinSeries.linear_right_summable, MeasureTheory.charFunDual_eq_prod_iff, EisensteinSeries.D2_S, Complex.abs_im_le_norm, Polynomial.int_cyclotomic_rw, Complex.tan_int_mul_pi_div_two, UnitAddTorus.mFourier_add, Complex.cpow_ofReal_re, PositiveLinearMap.preGNS_inner_def, CStarAlgebra.instNonnegSpectrumClassComplexNonUnital, UpperHalfPlane.cosh_dist, LSeries_eq_mul_integral_of_nonneg, NumberField.InfinitePlace.IsRamified.comap_embedding_conjugate, UpperHalfPlane.image_coe_closedBall, EisensteinSeries.G2_S_transform, Complex.angle_mul_right, PeriodPair.periodic_derivWeierstrassP, EisensteinSeries.summable_linear_left_mul_linear_left, Complex.re_sq_le_normSq, HurwitzZeta.oddKernel_def, Complex.div_im, Complex.im_nnratCast, Complex.tendsto_one_add_div_pow_exp, SchwartzMap.norm_fourierTransformCLM_toL2_eq, Complex.isIntegral_exp_rat_mul_pi_mul_I, SlashInvariantForm.sub_apply, Complex.natCast_mem_slitPlane, ArithmeticFunction.one_eq_delta, spectrum.gelfand_formula, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Complex.log_ofReal_mul, riemannZeta_eulerProduct_exp_log, Complex.norm_nnratCast, NumberField.Units.complexEmbedding_injective, IsSelfAdjoint.isConnected_spectrum_compl, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, Complex.norm_add_eq_iff, Real.fourier_mul_convolution_eq, Complex.cos_int_mul_two_pi_sub, VectorFourier.iteratedFDeriv_fourierIntegral, ModularForm.zero_apply, UpperHalfPlane.dist_coe_center, realPart_add_I_smul_imaginaryPart, ArithmeticFunction.LSeries_zeta_eq, Complex.iteratedDeriv_odd_sin, Polynomial.logMahlerMeasure_X_add_C, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, UpperHalfPlane.sigma_J, AddChar.forall_apply_eq_zero, Complex.equivRealProd_apply_le', EisensteinSeries.div_linear_zpow_differentiableOn, UnitAddTorus.mFourier_zero, Real.fourierIntegral_iteratedDeriv, Complex.sq_norm_sub_sq_im, CStarAlgebra.span_nonneg_inter_unitClosedBall, ProbabilityTheory.IsGaussian.charFun_eq', HurwitzZeta.cosZeta_one_sub, UpperHalfPlane.ofComplex_apply_of_im_pos, LSeriesSummable.le_const_mul_rpow, EulerSine.sin_pi_mul_eq, Complex.arg_neg_eq_arg_add_pi_iff, qExpansion_one, integral_mul_cexp_neg_mul_sq, jacobiTheta_S_smul, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, Complex.normSq_eq_norm_sq, VonNeumannAlgebra.centralizer_centralizer', CuspForm.coe_smul, Quaternion.coeComplex_zero, Complex.inv_cpow_eq_ite', StarAlgebra.elemental.bijective_characterSpaceToSpectrum, Complex.antilipschitz_equivRealProd, ModularForm.levelOne_weight_zero_rank_one, zeta_eq_tsum_one_div_nat_cpow, Complex.abs_im_eq_norm, Complex.I_pow_eq_pow_mod, Complex.ratCast_re, Complex.isPrimitiveRoot_iff, Complex.isometry_ofReal, Complex.norm_cpow_real, Complex.exp_periodic, gelfandTransform_map_star, Mathlib.Meta.Positivity.ofReal_nonneg, Complex.isTheta_ofReal, NumberField.mixedEmbedding.convexBodySumFun_smul, Complex.interior_preimage_im, Complex.logDeriv_sin, NumberField.mixedEmbedding.logMap_real_smul, Complex.isBigO_re_sub_re, AddChar.sum_apply_eq_zero_iff_ne_zero, norm_exp_mul_sq_le, Complex.comap_exp_nhdsNE, ProbabilityTheory.analyticAt_complexMGF, WeakFEPair.Îâ_eq, HurwitzZeta.hurwitzEvenFEPair_zero_symm, Complex.exp_nat_mul_two_pi_mul_I, CliffordAlgebraComplex.ofComplex_I, Complex.isBigO_cpow_rpow, Complex.log_exp_eq_sub_toIocDiv, UnitAddTorus.coeFn_mFourierLp, Complex.sinh_zero, UpperHalfPlane.denom_cocycle, Complex.norm_exp_sub_sum_le_norm_mul_exp, Complex.tan_sub', NumberField.mixedEmbedding.polarCoord_symm_apply, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, ModularForm.toSlashInvariantForm_coe, ProbabilityTheory.complexMGF_id_mul_I, Polynomial.intervalIntegrable_mahlerMeasure, Complex.deriv_Gamma_nat, Complex.HadamardThreeLines.norm_invInterpStrip, Complex.liftAux_neg_I, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst, Complex.isAlgebraic_sin_rat_mul_pi, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, UpperHalfPlane.coe_smul_of_det_pos, spectrum.map_pow, cfcâ_real_eq_complex, NumberField.InfinitePlace.isInfinitePlace, Complex.continuous_sinh, Complex.logDeriv_exp, Complex.ofReal_intCast, Complex.ofReal_add, ProbabilityTheory.complexMGF_gaussianReal, Complex.cpow_neg, bernoulli_zero_fourier_coeff, Complex.UnitDisc.coe_closedBall_smul, selfAdjoint.unitarySelfAddISMul_coe, Complex.isPrimitiveRoot_exp_of_isCoprime, ModularForm.instIsScalarTowerComplex, Circle.ext_iff, LSeriesSummable_zero, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, Complex.add_re, Complex.Gammaâ_eq_zero_iff, Complex.isOpen_compl_range_intCast, DirichletCharacter.LSeries.mul_mu_eq_one, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, Complex.hasSum_ofReal, CuspFormClass.zero_at_infty, CuspForm.coe_neg, HurwitzZeta.completedHurwitzZetaEven_residue_one, Complex.ofRealCLM_nnnorm, HurwitzZeta.hurwitzZetaEven_neg_two_mul_nat_add_one, Complex.imCLM_norm, hasDerivAt_jacobiThetaâ_fst, Polynomial.Chebyshev.T_complex_cosh, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, Complex.sinh_sq, UnitAddTorus.mFourier_neg, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, Polynomial.Chebyshev.C_two_mul_complex_cosh, Complex.HadamardThreeLines.interpStrip_scale, Complex.cpow_nat_mul, VectorFourier.fourierIntegral_convergent_iff, Complex.continuousOn_norm_circleTransformBoundingFunction, Complex.continuousAt_Gamma_one, intervalIntegral.intervalIntegrable_cpow, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, integral_exp_mul_I_eq_sinc, Complex.normSq_sub, Function.Periodic.im_invQParam, HurwitzZeta.cosZeta_eq, PeriodPair.differentiableOn_derivWeierstrassP, GaussianInt.toComplex_im_div, Complex.hasDerivAt_sinh, PeriodPair.weierstrassPExcept_def, Complex.sin_two_pi, UpperHalfPlane.norm_exp_two_pi_I_lt_one, NumberField.InfinitePlace.smul_coe_apply, PeriodPair.meromorphic_derivWeierstrassP, HurwitzZeta.hasSum_int_cosZeta, Complex.inv_re, Complex.arg_exp_mul_I, Complex.arg_of_re_neg_of_im_neg, DirichletCharacter.LFunction_eq_completed_div_gammaFactor, Complex.preimage_equivRealProd_prod, circleIntegrable_log_norm_factorizedRational, WeakFEPair.h_feq', Complex.isCauSeq_norm_exp, MeasureTheory.charFun_pi, SchwartzMap.convolution_apply, hasSum_jacobiThetaâ_term_fderiv, UpperHalfPlane.modular_S_smul, Complex.cos_add_pi, NumberField.mixedEmbedding.mem_span_latticeBasis, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaâ, Polynomial.mahlerMeasure_C_mul_X_add_C, Complex.tendsto_norm_tan_atTop, ProbabilityTheory.IsGaussian.charFunDual_eq_of_forall_strongDual_eq_zero, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, BoundedContinuousFunction.innerProbChar_apply, Complex.ofReal_prod, Complex.IsExpCmpFilter.tendsto_re, Circle.coe_inv_eq_conj, Complex.hasDerivAt_Gammaâ_one, Complex.analyticOnNhd_sin, Complex.hasSum_sin, Complex.tendsto_self_mul_Gamma_nhds_zero, riemannZeta_neg_two_mul_nat_add_one, SchwartzMap.integral_bilin_fourier_eq, Complex.det_conjAe, Complex.hasStrictDerivAt_const_cpow, Complex.sub_conj, Complex.sin_add_two_pi, PositiveLinearMap.toPreGNS_ofPreGNS, Orientation.kahler_neg_orientation, IsSelfAdjoint.cfc_arg, Complex.conj_im, EisensteinSeries.D2_inv, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, EisensteinSeries.hasSum_e2Summand_symmetricIco, ModularForm.eta_q_eq_cexp, ArithmeticFunction.convolution_vonMangoldt_const_one, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, intervalIntegral.integrableOn_Ioo_cpow_iff, SchwartzMap.fourierInv_apply_eq, Circle.coe_mul, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, SlashInvariantForm.exists_one_half_le_im_and_norm_le, Complex.arg_lt_pi_div_two_iff, Complex.arg_mul_cos_add_sin_mul_I_coe_angle, PeriodPair.weierstrassPExcept_zero, hasSum_jacobiThetaâ'_term, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, lipschitzWith_circleMap, Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, circleMap_notMem_ball, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, SlashInvariantFormClass.periodic_comp_ofComplex, integrableOn_Ioi_deriv_ofReal_cpow, HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat, PositiveLinearMap.exists_norm_apply_le, Real.fourierIntegral_real_eq_integral_exp_smul, Complex.map_exp_comap_re_atBot, Complex.intCast_re, fourier_coe_apply, Real.deriv_fourierIntegral, Complex.liftAux_I, Complex.interior_setOf_le_im, integral_exp_mul_I_eq_sin, norm_jacobiTheta_sub_one_le, Complex.sinh_neg, fourierSubalgebra_separatesPoints, Complex.isEquivalent_sinh, eisSummand_of_gammaSet_eq_divIntMap, ArithmeticFunction.convolution_vonMangoldt_zeta, Real.Angle.arg_toCircle, Complex.tan_add', MeasureTheory.SignedMeasure.re_toComplexMeasure, Complex.one_add_cpow_hasFPowerSeriesAt_zero, jacobiThetaâ'_add_right, HurwitzZeta.hasSum_nat_cosZeta, NumberField.mixedEmbedding.covolume_idealLattice, DirichletCharacter.LFunctionTrivChar_eq_mul_riemannZeta, ZMod.isPrimitive_stdAddChar, Complex.zero_im, Complex.tanh_eq_sinh_div_cosh, fourierCoeff.const_smul, NumberField.mixedEmbedding.volume_preserving_negAt, OnePoint.isZeroAt_iff_forall_SL2Z, NumberField.mixedEmbedding.normAtPlace_add_le, Complex.cos_add_sin_I, Complex.pow_cpow_ofNat_inv, Circle.coe_pow, Complex.tan_sub_int_mul_pi, HurwitzZeta.completedHurwitzZetaEven_eq, MeasureTheory.Lp.instFourierSMul, Complex.sin_eq_sin_iff, UpperHalfPlane.contMDiff_num, UpperHalfPlane.mdifferentiable_denom, Complex.arg_eq_zero_iff_zero_le, LSeries_convolution', UpperHalfPlane.dist_self_center, Complex.angle_eq_abs_arg, Complex.continuous_conj, LSeries.term_convolution, UpperHalfPlane.coe_mem_integerComplement, MeasureTheory.ComplexMeasure.integrable_rnDeriv, NumberField.mixedEmbedding.negAt_apply_isComplex, isBigO_riemannZeta_sub_one_div, ProbabilityTheory.isGaussian_iff_charFun_eq, Complex.ofReal_one, Complex.differentiableAt_exp, UpperHalfPlane.Ď_num, OnePoint.isBoundedAt_iff, Complex.conj_cpow, Complex.arg_zero, fourierIntegral_eq_half_sub_half_period_translate, LSeriesHasSum.smul, Complex.algHom_ext_iff, Complex.not_continuousAt_Gamma_zero, Complex.differentiable_Gammaâ_inv, RCLike.sqrt_complex, continuous_circleMap, differentiableAt_jacobiThetaâ_fst, Complex.equivRealProdAddHom_symm_apply_re, Complex.iter_deriv_exp, HasProdLocallyUniformlyOn_euler_sin_prod, NormedSpace.ofReal_exp_â_â, Complex.sq_nonneg_iff, convex_halfSpace_im_lt, Complex.sin_pi_sub, ModularForm.one_coe_eq_one, VonNeumannAlgebra.mem_carrier, Complex.differentiableAt_tan, has_antideriv_at_fourier_neg, Complex.ofReal_nnratCast, UnitAddTorus.mFourier_norm, CStarModule.norm_inner_le, Complex.UnitDisc.instCanLiftCoeLtRealNormOfNat, Complex.equivRealProdAddHom_symm_apply_im, VonNeumannAlgebra.centralizer_centralizer, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, LSeriesSummable.sum, Complex.selfAdjointEquiv_apply, Function.Periodic.continuous_qParam, UpperHalfPlane.im_smul, NumberField.IsCMField.complexEmbedding_complexConj, Complex.range_liftAux, Complex.HadamardThreeLines.interpStrip_eq_of_pos, UpperHalfPlane.normSq_denom_pos, HurwitzZeta.hasSum_expZeta_of_one_lt_re, Complex.sin_three_mul, UniformContinuousOn.cexp, Polynomial.one_le_mahlerMeasure_of_ne_zero, Complex.exp_neg, eqOn_iteratedDerivWithin_cotTerm_upperHalfPlaneSet, Complex.neg_iff, Complex.inv_cpow_eq_ite, Complex.liftAux_apply_I, OnePoint.IsZeroAt.smul_iff, Complex.continuous_exp, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, StarSubalgebra.spectrum_eq, EisensteinSeries.e2Summand_zero_eq_two_riemannZeta_two, ModularFormClass.exp_decay_sub_atImInfty, Complex.frontier_preimage_im, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, ModularForm.sub_apply, EisensteinSeries.linear_left_summable, Complex.inv_cpow, ModularFormClass.exists_petersson_le, PeriodPair.hasSumLocallyUniformly_weierstrassPExcept, Circle.invOn_arg_exp, UpperHalfPlane.coe_smul, Complex.inv_def, Complex.equivRealProdLm_apply, Complex.div_intCast, CStarAlgebra.linear_combination_nonneg, Complex.IsExpCmpFilter.tendsto_norm, Complex.hasDerivAt_cos, ZMod.invDFT_def', completedRiemannZeta_eq, Complex.cosh_zero, Complex.ofRealCLM_apply, UpperHalfPlane.ofComplex_apply_eq_of_im_nonpos, Complex.log_sub_self_isBigO, differentiableAt_complex_iff_differentiableAt_real, cfcHom_real_eq_restrict, NumberField.ComplexEmbedding.IsConj.isReal_comp, jacobiThetaâ'_neg_left, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Complex.arg_neg_eq_arg_add_pi_of_im_neg, Complex.arg_conj, inner_map_complex, ModularForm.ext_iff, Complex.cosh_sq, BoundedContinuousFunction.probCharDual_zero, MeasureTheory.charFun_conv, Complex.arg_eq_nhds_of_im_neg, LSeriesHasSum.add, Complex.cos_sub_nat_mul_two_pi, GaussianInt.toComplex_add, CStarMatrix.toCLM_apply_single, Real.fourier_fderiv, Complex.cos_int_mul_two_pi_add_pi, Complex.tendsto_exp_comap_re_atBot, Complex.normSq_ofNat, IsSelfAdjoint.spectrumRestricts, Complex.mul_cpow_ofReal_nonneg, NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset, Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots, imaginaryPart.norm_le, Circle.instContinuousSMul, eqOn_iteratedDeriv_cotTerm, VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip, tsum_riemannZetaSummand, NumberField.mixedEmbedding.convexBodySumFun_neg, Complex.restrictScalars_one_smulRight, SlashInvariantForm.coe_sub, Complex.exp_list_sum, Complex.summable_ofReal, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, hasDerivAt_fourier_neg, Complex.nonpos_iff, VectorFourier.fderiv_fourierIntegral, Algebra.norm_complex_eq, fourier_eval_zero, SchwartzMap.fourierInv_lineDerivOp_eq, VectorFourier.integral_fourierIntegral_swap, GaussianInt.toComplex_sub, Complex.cos_two_mul', Complex.tendsto_euler_sin_prod, Complex.arg_of_im_nonneg_of_ne_zero, ModularForm.const_toFun, MeasureTheory.integral_charFun_Icc, ZMod.completedLFunction_eq, Complex.normSq_ofReal_add_I_mul_sqrt_one_sub, Complex.sqrt_zero, linear_isometry_complex, CFC.log_monotoneOn, UnitAddTorus.orthonormal_mFourier, Complex.dist_of_im_eq, Complex.exp_ofReal_mul_I_im, NumberField.mixedEmbedding.convexBodySumFun_continuous, LSeriesSummable.neg_iff, Fourier.fourierIntegral_const_smul, Complex.zero_cpow_eq_iff, Complex.cos_surjective, HurwitzZeta.completedSinZeta_one_sub, CStarMatrix.toCLM_apply_eq_sum, GaussianInt.toComplex_star, UpperHalfPlane.dist_eq, EulerSine.integral_sin_mul_sin_mul_cos_pow_eq, Circle.star_addChar, analyticOnNhd_cexp, HurwitzZeta.hurwitzZeta_residue_one, Complex.tan_zero, isBigO_at_im_infty_jacobiTheta_sub_one, WithCStarModule.pi_norm, Polynomial.mahlerMeasure_X_add_C, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Complex.conjAe_coe, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, OnePoint.isBoundedAt_infty_iff, fourierCoeff_toLp, IsSelfAdjoint.toReal_spectralRadius_complex_eq_norm, GaussianInt.toComplex_def, ProbabilityTheory.hasDerivAt_complexMGF, AddChar.card_eq, ProbabilityTheory.IsGaussian.charFunDual_eq, coe_fourierBasis, Complex.tsum_exp_neg_quadratic, CFC.monotone_rpow, AddChar.doubleDualEmb_bijective, Complex.ofReal_comp_add, ModularFormClass.qExpansion_coeff, Polynomial.mahlerMeasure_mul, ZMod.dft_apply, CuspForm.coe_translate, Complex.norm_real, CuspFormClass.petersson_bounded_right, ModularFormClass.bdd_at_infty, UpperHalfPlane.norm_qParam_lt_one, OnePoint.IsZeroAt.add, PeriodPair.derivWeierstrassP_sub_coe, Complex.conj_mul', riemannZeta_zero, Complex.range_arg, Complex.isAddQuotientCoveringMap_exp, inr_comp_cfcâHom_eq_cfcâAux, rotationOf_rotation, Complex.measurable_cos, CFC.monotoneOn_one_sub_one_add_inv_real, skewAdjoint.negISMul_apply_coe, SpectrumRestricts.real_iff, Complex.log_mul_eq_add_log_iff, Complex.cot_pi_eq_exp_ratio, Complex.sin_conj, GaussianInt.to_real_re, torusIntegral_const_mul, HurwitzZeta.differentiableAt_completedHurwitzZetaEven, Complex.cosh_eq_tsum, LSeries.norm_term_eq, Complex.I_pow_four, ProbabilityTheory.norm_complexMGF_le_mgf, Complex.inv_zero, ModularFormClass.exists_bound, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, ModularForm.neg_apply, EisensteinSeries.auxbound1, Complex.rank_real_complex', Polynomial.logMahlerMeasure_def, Complex.frontier_setOf_lt_im, Polynomial.logMahlerMeasure_X, Complex.conj_eq_iff_re, Complex.integral_exp_neg_mul_rpow, ModularForm.eq_const_of_weight_zero, Complex.slitPlane_eq_union, Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod, Complex.isIntegral_two_mul_sin_rat_mul_pi, CStarMatrix.ofMatrix_eq_ofMatrixL, Complex.interior_reProdIm, HurwitzZeta.differentiableAt_one_completedHurwitzZetaEven_sub_completedHurwitzZetaEven, UpperHalfPlane.denom_J, CommCStarAlgebra.toStarModule, Complex.ofReal_sum, Complex.mul_I_re, Complex.contDiff_exp, HurwitzZeta.hurwitzZetaEven_one_sub, Real.fourier_eq, Complex.closure_preimage_re, Complex.nndist_of_re_eq, ProbabilityTheory.indepFun_iff_charFunDual_prod', le_radius_cauchyPowerSeries, Complex.normSq_zero, Complex.isOpenQuotientMap_pow, HurwitzZeta.hasSum_int_sinKernel, LSeries.term_sub_apply, ZMod.invDFT_apply', HurwitzZeta.completedCosZetaâ_one_sub, qExpansion_sub, SchwartzMap.fourier_evalCLM_eq, SlashInvariantForm.coe_prod, SlashInvariantForm.coe_natCast, Complex.interior_setOf_im_le, Complex.ofReal_comp_mul, EisensteinSeries.norm_le_tsum_norm, hasMellin_one_Ioc, NumberField.canonicalEmbedding.nnnorm_eq, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, Complex.norm_ratCast, QuasispectrumRestricts.real_iff, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Complex.tan_mul_cos, TemperedDistribution.instLineDerivSMulReal, Complex.two_cosh, Complex.HadamardThreeLines.interpStrip_eq_of_zero, Complex.norm_of_nonneg, Complex.conj_cpow_eq_ite, Complex.abs_im_lt_norm, UpperHalfPlane.ofComplex_apply_eq_ite, MeasureTheory.Measure.toTemperedDistribution_apply, Complex.sin_antiperiodic, tendsto_integral_exp_smul_cocompact_of_inner_product, HurwitzZeta.completedCosZeta_residue_zero, HurwitzZeta.LSeriesHasSum_exp, CStarMatrix.toCLM_apply, DirichletCharacter.convolution_twist_vonMangoldt, Complex.ofReal_comp_balance, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, HurwitzZeta.completedHurwitzZetaEven_one_sub, bernoulliFourierCoeff_eq, UpperHalfPlane.qParam_tendsto_atImInfty, Complex.sinh_two_mul, summable_dirichletSummand, NumberField.mixedEmbedding.norm_nonneg, Complex.cosh_two_mul, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, Complex.ofReal_nsmul, Complex.cos_add, Complex.norm_mul_cos_add_sin_mul_I, Complex.isPrimitiveRoot_exp_of_coprime, Complex.normSq_conj, Complex.tan_sub_nat_mul_pi, Complex.differentiable_sin, Complex.inv_natCast_cpow_ofReal_pos, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, Complex.continuous_normSq, PeriodPair.weierstrassP_add_coe, periodic_circleMap, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, ModularForm.logDeriv_eta_eq_E2, Complex.cosh_sub, TemperedDistribution.fourier_lineDerivOp_eq, Complex.sin_eq_one_iff, ModularForm.coe_eq_zero_iff, Complex.equivRealProdLm_symm_apply, Complex.norm_zpow, MeasureTheory.charFunDual_map_const_add, span_selfAdjoint, MeasureTheory.charFunDual_map_add_const, TemperedDistribution.fourier_delta_zero, Complex.equivRealProdLm_symm_apply_im, PeriodPair.instProperSpaceSubtypeComplexMemSubmoduleIntLattice, Complex.add_conj, Complex.coe_basisOneI_repr, Complex.volume_sum_rpow_lt, realPart_I_smul, Complex.analyticOn_cos, ModularForm.coeHom_apply, circleMap_mem_sphere, Complex.tanh_conj, MeromorphicNFOn.Gamma, selfAdjoint.realPart_unitarySelfAddISMul, Complex.hasDerivAt_logTaylor, DirichletCharacter.differentiable_LFunction, ModularGroup.tendsto_normSq_coprime_pair, HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_nat, LSeriesSummable.add, NumberField.mixedEmbedding.norm_smul, ModularForm.slash_action_eq'_iff, circleMap_preimage_codiscrete, PositiveLinearMap.gnsStarAlgHom_apply, Real.fourier_iteratedDeriv, Complex.abs_arg_inv, Complex.normSq_intCast, Complex.cos_periodic, GaussianInt.to_real_im, surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar, NumberField.InfinitePlace.IsRamified.comap_embedding, Complex.lintegral_comp_polarCoord_symm, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, NumberField.mixedEmbedding.span_latticeBasis, NumberField.InfinitePlace.LiesOver.embedding_comp_eq_or_conjugate_embedding_comp_eq, ProbabilityTheory.indepFun_iff_charFun_prod, zero_cpow_eq_nhds, WeakFEPair.hf_zero, Complex.cpow_mul_nat, spectrum.nonempty, Circle.leftInverse_exp_arg, LSeries.abscissaOfAbsConv_add_le, Complex.exp_pi_div_two_mul_I, Complex.measurable_im, Complex.continuousAt_ofReal_cpow, EisensteinSeries.linear_inv_isBigO_right_add, circleMap_mem_closedBall, LinearMap.isPositive_iff_complex, GaussianInt.toComplex_re_div, VectorFourier.fourierSMulRight_apply, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, UpperHalfPlane.petersson_norm_symm, Complex.instSMulCommClassOfReal, integral_cexp_quadratic, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, NumberField.mixedEmbedding.measurableSet_fundamentalCone, Complex.GammaSeq_add_one_left, NumberField.mixedEmbedding.polarCoord_source, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, UpperHalfPlane.J_smul, Real.circleAverage_eq_circleAverage_zero_one, Complex.orthonormalBasisOneI_repr_symm_apply, SlashInvariantForm.slash_action_eqn'', Mathlib.Meta.Positivity.ofReal_pos, HurwitzZeta.sinZeta_two_mul_nat_add_one', MeasureTheory.norm_charFun_le_one, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, hasDerivAt_circleMap, Complex.tan_eq_sin_div_cos, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, ModularFormClass.qExpansion_coeff_zero, Complex.tan_sub_pi, GaussianInt.toComplex_re, imaginaryPart_apply_coe, Complex.UnitDisc.instSMulCommClass_closedBall_right, Complex.measurable_exp, Complex.Gammaâ_def, EisensteinSeries.eisensteinSeries_SIF_apply, UnitAddTorus.hasSum_mFourier_series_L2, Complex.norm_mul_exp_arg_mul_I, CFC.rpow_le_rpow, Complex.cpow_natCast, Complex.dist_eq, Complex.tan_add_pi, Complex.cpow_inv_two_im_eq_sqrt, LSeries_one_eq_riemannZeta, TemperedDistribution.laplacian_eq_sum, spectrum_subset_unitary_of_mem_unitary, WithCStarModule.pi_inner, NumberField.mixedEmbedding.continuous_norm, Complex.cpow_inv_two_re, CuspForm.coe_sub, NumberField.discr_eq_basisMatrix_det_sq, LSeries.term_neg_apply, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, Complex.continuousOn_tan, ZMod.dft_comp_neg, Complex.iteratedDeriv_add_one_sinh, NumberField.mixedEmbedding.det_matrixToStdBasis, Complex.im_balance, Complex.ofReal_expect, Complex.isPrimitiveRoot_exp_rat_of_even_num, AddChar.starComp_apply, TemperedDistribution.instContinuousLineDeriv, RCLike.complexLinearIsometryEquiv_symm_apply, Complex.zero_cpow, Complex.iteratedDeriv_even_cos, WithCStarModule.prod_norm, UpperHalfPlane.denom_neg, Complex.div_re, hasDerivAt_fourier, Filter.Tendsto.ofReal, CuspForm.neg_apply, Complex.iteratedDeriv_add_one_sin, Complex.sin_sq_add_cos_sq, Complex.continuousAt_cpow_zero_of_re_pos, Circle.norm_coe, NumberField.mixedEmbedding.polarSpaceCoord_symm_apply, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, HurwitzZeta.completedHurwitzZetaOdd_neg, Complex.UnitDisc.instIsScalarTower_closedBall, Complex.volume_preserving_equiv_real_prod, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, Complex.sinh_add, Complex.instCompleteSpace, Real.fourier_bilin_convolution_eq, UpperHalfPlane.le_dist_coe, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, CStarMatrix.mul_entry_mul_eq_inner_toCLM, Complex.isPrimitiveRoot_exp, GaussianInt.toComplex_inj, fourier_apply, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ModularForm.logDeriv_one_sub_cexp, Complex.HadamardThreeLines.diffContOnCl_interpStrip, Complex.isIntegral_exp_neg_rat_mul_pi_mul_I, Complex.arg_eq_arg_iff, CliffordAlgebraComplex.equiv_symm_apply, Complex.angle_div_left_eq_angle_mul_right, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, HurwitzZeta.hasSum_nat_completedSinZeta, circleMap_zero, Complex.cot_conj, integrableOn_exp_mul_complex_Iic, Complex.zero_lt_real, SchwartzMap.integral_sesq_fourierIntegral_eq, Real.fourierIntegral_eq', EisensteinSeries.isBigO_linear_add_const_vec, Complex.frontier_setOf_le_re, DirichletCharacter.LSeriesSummable_iff, CStarModule.norm_sq_eq, Complex.norm_natCast_cpow_of_pos, hasFPowerSeriesOn_cauchy_integral, NumberField.InfinitePlace.embedding_of_isReal_apply, UpperHalfPlane.contMDiff_denom_zpow, contDiffOn_tsum_cexp, convex_halfSpace_re_ge, Complex.Gammaâ_add_one, deriv_circleMap, Complex.cos_add_pi_div_two, Algebra.leftMulMatrix_complex, PeriodPair.latticeBasis_one, EisensteinSeries.auxbound2, NormedRing.algEquivComplexOfComplete_symm_apply, Complex.norm_div, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', Polynomial.X_pow_sub_X_sub_one_irreducible_aux, NonUnitalCommCStarAlgebra.toStarModule, qExpansion_add, Complex.analyticAt_sinh, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, Complex.hasStrictDerivAt_cos, NumberField.mixedEmbedding.covolume_integerLattice, Orientation.kahler_apply_self, Complex.frontier_setOf_re_lt, PeriodPair.weierstrassP_sub_coe, Complex.analyticOn_univ_iff_differentiable, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, Complex.conjCLE_nnorm, fourierIntegral_gaussian_innerProductSpace, LSeries.term_delta, Real.circleAverage_smul, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, ProbabilityTheory.HasGaussianLaw.charFun_map_eq, UpperHalfPlane.petersson_symm, Complex.iteratedDeriv_add_one_cos, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, Complex.isBigO_im_sub_im, cexp_neg_quadratic_isLittleO_abs_rpow_cocompact, ArithmeticFunction.LSeries_vonMangoldt_eq, HurwitzZeta.hurwitzOddFEPair_fâ, WithCStarModule.inner_single_right, EisensteinSeries.qExpansion_identity_pnat, Complex.sqrt_neg_one, circleMap_zero_mul, LSeries.abscissaOfAbsConv_convolution_le, Real.iteratedDeriv_fourier, Complex.isCoveringMapOn_exp, UpperHalfPlane.petersson_slash_SL, riemannZeta_pos_of_one_lt, selfAdjoint.star_coe_unitarySelfAddISMul, Orientation.kahler_rotation_left', zeta_eq_tsum_one_div_nat_add_one_cpow, Complex.continuous_cos, DirichletCharacter.differentiableAt_completedLFunction, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, Complex.cpow_one, CliffordAlgebraComplex.toComplex_Κ, UpperHalfPlane.Ď_ofReal, Complex.Gammaâ_one, convex_halfSpace_im_ge, LSeries.term_add_apply, Complex.ofReal_eq_zero, rotation_trans, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, NumberField.mixedEmbedding.convexBodyLT_neg_mem, UpperHalfPlane.le_dist_iff_le_dist_coe_center, Complex.nnnorm_ofNat, Complex.linearEquiv_det_conjAe, Complex.ofReal_zero, SlashInvariantForm.toFun_eq_coe, NumberField.mixedEmbedding.polarCoord_target, Complex.continuousAt_arg_coe_angle, EisensteinSeries.r_mul_max_le, Complex.norm_exp_ofReal, Complex.digamma_def, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', ModularForm.SL_slash_def, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, Complex.div_ofReal, Complex.Gamma_mul_Gamma_eq_betaIntegral, NumberField.Units.complexEmbedding_apply, PeriodPair.hasSum_weierstrassP, convex_halfSpace_re_lt, NumberField.count_multisetInfinitePlace_eq_mult, LSeriesSummable.smul_iff, UpperHalfPlane.ofComplex_apply, Complex.instStarModuleReal, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, PeriodPair.coeff_weierstrassPSeries, DirichletCharacter.absicssaOfAbsConv_eq_one, Complex.ball_one_subset_slitPlane, PeriodPair.isOpen_compl_lattice_diff, Complex.restrictScalars_toSpanSingleton, Orientation.normSq_kahler, Complex.norm_prime_cpow_le_one_half, Complex.volume_closedBall, Complex.tendsto_one_add_div_cpow_exp, Complex.nnnorm_nnratCast, Complex.hasSum_cos', Complex.closure_setOf_re_lt, Complex.deriv_cosh, Polynomial.Chebyshev.U_complex_cosh, Complex.normSq_inv, ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul, PeriodPair.derivWeierstrassP_coe, Complex.cos_add_cos, Complex.stolzCone_subset_stolzSet_aux, ZMod.dft_dft, locallyFinsuppWithin.logCounting_divisor, Complex.arg_div_coe_angle, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.mixedEmbedding.negAt_symm, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg, AddChar.coe_doubleDualEquiv, jacobiThetaâ'_add_left', fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, Complex.norm_ofNat, Polynomial.toAddCircle_monomial_eq_smul_fourier, Complex.inner, jacobiThetaâ'_functional_equation, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, continuousAt_const_cpow', mellin_comp_inv, NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem, Complex.isTheta_ofReal_right, Complex.hasStrictDerivAt_sin, Complex.polarCoord_source, Polynomial.sum_sq_norm_coeff_eq_circleAverage, riemannZeta_one, Complex.expMonoidHom_apply, Complex.coe_imAddGroupHom, MulChar.star_apply', Polynomial.mahlerMeasure_X_sub_C, SlashInvariantForm.coe_zero, LSeries.term_neg, Complex.cos_sq_add_sin_sq, Complex.contDiffAt_tan, HurwitzZeta.hurwitzOddFEPair_Îľ, NumberField.mixedEmbedding.polarCoord_symm_eq, Complex.analyticWithinAt_sinh, Complex.analyticOnNhd_cosh, UpperHalfPlane.coe_J_smul, Complex.exp_sub_sum_range_succ_isLittleO_pow, Complex.normSq_div, ModularForm.IsGLPos.coe_smul, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, Complex.continuousOn_prod_circle_transform_function, Complex.pow_cpow_nat_inv, ProbabilityTheory.integrable_cexp_mul_of_re_mem_interior_integrableExpSet, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, Complex.natCast_cpow_natCast_mul, MeasureTheory.measureReal_abs_gt_le_integral_charFun, Complex.log_div_self, HasDerivAt.ofReal_comp, UpperHalfPlane.dist_center_dist, NumberField.conj_basisMatrix, Complex.normSq_ofReal, DifferentiableAt.ofReal_cpow_const, Complex.isBigO_ofReal_left, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Complex.sin_pi_div_two, hasFDerivAt_jacobiThetaâ, Complex.isHomeomorphicTrivialFiberBundle_re, NumberField.mixedEmbedding.polarSpaceCoord_target', Complex.sin_periodic, Complex.im_comp_balance, RCLike.complexRingEquiv_symm_apply, Real.abs_circleAverage_le_circleAverage_abs, Complex.instNontrivial, Complex.GammaSeq_eq_betaIntegral_of_re_pos, PeriodPair.sumInvPow_zero, rotationOf_coe, Complex.cos_sub_pi_div_two, Algebra.norm_complex_apply, Complex.UnitDisc.coe_mul, NumberField.mixedEmbedding.convexBodyLT'_volume, CircleIntegrable.sum, Complex.deriv_tan, Complex.norm_def, NumberField.InfinitePlace.isometry_embedding_of_isReal, UpperHalfPlane.dist_le_dist_coe_div_sqrt, OnePoint.IsBoundedAt.smul_iff, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, Complex.abs_im_div_norm_le_one, Complex.norm_int_of_nonneg, Complex.cos_zero, Complex.hasDerivAt_cosh, circleMap_zero_div, CuspFormClass.exists_bound, EisensteinSeries.tendsto_zero_inv_linear, Unitization.nnreal_cfcâ_eq_cfc_inr, NumberField.ComplexEmbedding.place_conjugate, Complex.IsExpCmpFilter.isLittleO_log_norm_re, Complex.sqrt_map, Complex.cpow_ofNat_mul, circleAverage_log_norm_add_const_eq_posLog, Complex.UnitDisc.coe_smul_closedBall, Complex.norm_natCast_cpow_pos_of_pos, LSeries.term_of_ne_zero', Complex.re_le_norm, HurwitzZeta.differentiableAt_hurwitzZeta, Complex.norm_add_mul_I, NumberField.inverse_basisMatrix_mulVec_eq_repr, TemperedDistribution.fourierTransform_apply, Complex.equivRealProdAddHom_apply, Complex.contDiff_sinh, Complex.arg_neg_one, Complex.interior_setOf_re_le, DirichletCharacter.deriv_LFunctionTrivCharâ_apply_of_ne_one, Complex.abs_re_le_norm, LSeries.term_add, Complex.instIsAddTorsionFree, NumberField.InfinitePlace.card_real_embeddings, Complex.isOpen_im_gt_EReal, ZMod.completedLFunction_const_mul, CStarModule.norm_eq_csSup, LSeriesSummable.convolution, Complex.tan_int_mul_pi_sub, jacobiThetaâ_undef, ModularForm.IsGLPos.smul_apply, SlashInvariantForm.coe_trace, isConformalMap_complex_linear_conj, mellin_comp_rpow, Polynomial.Chebyshev.T_complex_cos, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, LSeries_differentiableOn, Complex.cos_add_mul_I, IsSelfAdjoint.spectralRadius_eq_nnnorm, Complex.GammaIntegral_one, differentiableAt_riemannZeta, Complex.div_ofNat_re, Complex.tendsto_partialGamma, Complex.exp_sub_sum_range_isBigO_pow, riemannZeta_eulerProduct, Complex.isOpenQuotientMap_zpow_compl_zero, DirichletCharacter.norm_LFunction_product_ge_one, UpperHalfPlane.eventuallyEq_coe_comp_ofComplex, Complex.IsExpCmpFilter.isLittleO_zpow_mul_exp, EisensteinSeries.summable_linear_sub_mul_linear_add, Complex.measurableEquivPi_symm_apply, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, Complex.I_pow_three, Complex.instIsCentralScalarOfReal, Orientation.kahler_rightAngleRotation_left, SlashInvariantForm.coe_neg, LSeriesSummable_one_iff, Orientation.kahler_comp_linearIsometryEquiv, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, Real.fourierIntegral_fderiv, Function.Periodic.invQParam_tendsto, Complex.exp_sub_cosh, cfcâHom_real_eq_restrict, PeriodPair.latticeEquiv_symm_apply, Complex.equivRealProdLm_symm_apply_re, Complex.UnitDisc.mk_zero, Complex.tanh_mul_I, MeasureTheory.ComplexMeasure.im_apply, Complex.im_nsmul, Complex.closure_setOf_lt_re, UnitAddTorus.mFourierSubalgebra_separatesPoints, Complex.betaIntegral_convergent, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, NumberField.mixedEmbedding.normAtPlace_neg, EisensteinSeries.linear_isTheta_left, Complex.coe_algebraMap, Complex.enorm_exp_I_mul_ofReal, Real.fourierIntegral_convergent_iff, Complex.cos_int_mul_two_pi_sub_pi, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, CuspForm.ext_iff, PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept, CStarMatrix.ofMatrix_eq_ofMatrixStarAlgEquiv, SlashInvariantForm.slash_action_eqn_SL'', Complex.cos_add_two_pi, AddChar.starComp_eq_inv, Complex.ofReal_comp_pow, LSeries_sum, UpperHalfPlane.comp_ofComplex_of_im_le_zero, NumberField.mixedEmbedding.unitSMul_smul, Complex.hasDerivAt_sin, fourierCoeff_eq_intervalIntegral, NumberField.mixedEmbedding.continuous_normAtPlace, analyticOn_cexp, Complex.closure_reProdIm, Real.hasDerivAt_fourierChar, MeasureTheory.norm_one_sub_charFun_le_two, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, circleIntegral.integral_sub_zpow_of_ne, Orientation.kahler_rotation_left, multipliable_sineTerm, LindemannWeierstrass.integral_exp_mul_eval, Complex.isUniformEmbedding_ofReal, GaussianInt.intCast_real_norm, Complex.conjCLE_enorm, LSeries_one_mul_Lseries_moebius, MeasureTheory.charFunDual_eq_pi_iff, Complex.exists_norm_mul_eq_self, DirichletCharacter.LSeries_eulerProduct_hasProd, MellinConvergent.comp_rpow, Complex.hasSum_conj, Complex.re_qsmul, LSeriesHasSum.sub, PeriodPair.deriv_derivWeierstrassPExcept_self, WeakFEPair.functional_equationâ, NormedRing.algEquivComplexOfComplete_apply, SchwartzMap.inner_fourierTransformCLM_toL2_eq, CFC.nnrpow_le_nnrpow, Complex.ofReal_injective, Real.tendsto_integral_cexp_sq_smul, Complex.UnitDisc.coe_injective, inner_map_self_eq_zero, Complex.hasStrictDerivAt_exp, Complex.IsExpCmpFilter.isLittleO_im_pow_exp_re, Complex.card_primitiveRoots, Real.enorm_exp_I_mul_ofReal_sub_one_le, Real.iteratedFDeriv_fourier, Complex.div_intCast_re, NumberField.mixedEmbedding.indexEquiv_apply_isReal, NumberField.ComplexEmbedding.Extension.comp_eq, EisensteinSeries.q_expansion_bernoulli, SchwartzMap.convolution_continuous_left, IsStarNormal.instContinuousFunctionalCalculus, Polynomial.mahlerMeasure_one, UpperHalfPlane.coe_specialLinearGroup_apply, circleIntegral.integral_smul_const, Complex.hasStrictDerivAt_cosh, Cardinal.mk_univ_complex, HurwitzZeta.cosKernel_def, Complex.GammaAux_recurrence1, LSeries_add, Complex.ofReal_mem_slitPlane, CStarAlgebra.span_nonneg_inter_closedBall, LSeries_delta, Complex.I_mul, LSeries.term_smul_apply, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, Complex.sin_add, SchwartzMap.integral_fourier_mul_eq, Complex.arg_of_im_neg, Complex.I_mul_re, Complex.normSq_nonneg, GaussianFourier.tendsto_verticalIntegral, CuspForm.instIsScalarTowerComplex, Complex.measurable_sinh, Complex.volume_preserving_equiv_pi, Complex.wedgeIntegral_add_wedgeIntegral_eq, EisensteinSeries.D2_one, Complex.norm_sub_one_sq_eqOn_sphere, Complex.logTaylor_zero, AEMeasurable.complex_ofReal, Complex.UnitDisc.continuous_coe, Complex.sqrt_neg_I, Complex.abs_arg_lt_pi_div_two_iff, HurwitzZeta.sinZeta_two_mul_nat_add_one, GaussianInt.toComplex_im, GaussianInt.im_toComplex, NumberField.ComplexEmbedding.IsReal.comp, not_countable_complex, differentiableAt_const_cpow_of_neZero, Complex.im_sum, ValueDistribution.proximity_zero_of_complexValued, tsum_dirichletSummand, Real.hasFDerivAt_fourierIntegral, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex, Complex.sqrt_eq_real_add_ite, NumberField.mixedEmbedding.normAtPlace_apply, linearEquiv_det_rotation, Complex.coe_selfAdjointEquiv, NumberField.ComplexEmbedding.lift_comp_algebraMap, Polynomial.Chebyshev.S_two_mul_complex_cosh, ModularFormClass.levelOne_weight_zero_const, Complex.dist_conj_conj, circleIntegrable_sub_zpow_iff, ArithmeticFunction.LSeries_zeta_eq_riemannZeta, Complex.ext_norm_arg_iff, Polynomial.fourierCoeff_toAddCircle_natCast, Polynomial.mahlerMeasure_zero, Complex.not_le_zero_iff, Complex.conjCLE_apply, Complex.nnnorm_natCast, Complex.LogDeriv_exp, Complex.log_mul, norm_jacobiThetaâ'_term_le, completedRiemannZetaâ_one, Complex.arg_conj_coe_angle, NumberField.mixedEmbedding.volume_eq_zero, Circle.coe_eq_one, Complex.nndist_conj_self, Complex.differentiable_one_div_Gamma, imaginaryPart_ofReal, Complex.cos_neg, Complex.eq_zero_cpow_iff, ModularGroup.im_smul_eq_div_normSq, Complex.pos_iff, HurwitzZeta.hurwitzZetaOdd_eq, UpperHalfPlane.cosh_half_dist, SchwartzMap.lineDerivOp_fourierInv_eq, finrank_real_of_complex, CliffordAlgebraComplex.equiv_apply, Complex.arg_mul_real, Complex.integerComplement_eq, NumberField.mixedEmbedding.stdBasis_apply_isReal, DirichletCharacter.LSeries_eulerProduct_exp_log, Complex.not_differentiableAt_Gamma_zero, Complex.sin_eq, Real.fourierChar_apply, NumberField.canonicalEmbedding.norm_le_iff, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, StarSubalgebra.mem_spectrum_iff, ProbabilityTheory.differentiableOn_complexMGF, Complex.arg_mul, Real.fourier_bilin_convolution_eq_integral, Complex.coe_smul, PeriodPair.deriv_weierstrassPExcept_same, MeasureTheory.ComplexMeasure.equivSignedMeasureâ_symm_apply, NumberField.mixedEmbedding.normAtPlace_apply_of_isComplex, Function.Periodic.qParam_tendsto, continuousAt_jacobiTheta, Complex.div_ratCast_im, PeriodPair.analyticOnNhd_derivWeierstrassP, Complex.Gammaâ_residue_zero, Complex.lift_symm_apply_coe, integrableOn_Ioi_cpow_of_lt, GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I, NumberField.mixedEmbedding_injective, EulerSine.antideriv_cos_comp_const_mul, Complex.instTietzeExtension, Complex.re_eq_neg_norm, NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff, NumberField.mixedEmbedding.convexBodyLT_convex, Real.tendsto_integral_exp_smul_cocompact, Complex.instT2Space, mellin_convergent_iff_norm, MulChar.star_eq_inv, UpperHalfPlane.exp_half_dist, ArithmeticFunction.LSeriesSummable_moebius_iff, Complex.normSq_add_mul_I, Orientation.kahler_mul, GaussianFourier.integral_cexp_neg_mul_sum_add, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat_sub_one, Complex.continuous_ofReal_cpow_const, LSeriesHasSum_one, ModularFormClass.qExpansion_coeff_eq_circleIntegral, ProbabilityTheory.isGaussian_iff_charFunDual_eq, CuspForm.coe_zero, EisensteinSeries.linear_isTheta_right_add, Complex.neg_re, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, NormedAlgebra.Real.nonempty_algEquiv_or, ModularForm.coe_prod, HurwitzZeta.differentiableAt_completedCosZeta, fourier_neg, Complex.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, fourierIntegral_gaussian, Algebra.trace_complex_apply, ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, PeriodPair.meromorphic_weierstrassP, EisensteinSeries.tendsto_double_sum_S_act, WeakDual.CharacterSpace.mem_spectrum_iff_exists, Complex.conj_re, Complex.arg_inv, Complex.im_mul_ofReal, circleAverage_log_norm_sub_const_eq_posLog, Complex.sinh_eq_tsum, Complex.sin_add_int_mul_two_pi, continuousAt_jacobiThetaâ, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, injOn_circleMap_of_abs_sub_le, Complex.im_eq_sub_conj, Polynomial.isOpenQuotientMap_eval, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, CStarAlgebra.rpow_neg_one_le_one, EulerSine.antideriv_sin_comp_const_mul, PeriodPair.analyticAt_derivWeierstrassPExcept, Complex.zero_le_real, Complex.differentiableAt_cosh, Complex.norm_exp, Complex.lim_im, Complex.div_natCast_im, Complex.cot_eq_cos_div_sin, ModularForm.smul_apply, UpperHalfPlane.coe_injective, Complex.ofReal_natCast, GaussianInt.toComplex_neg, MeasureTheory.charFun_zero_measure, Complex.differentiableAt_Gamma_nat_add_one, TemperedDistribution.instFourierInvSMul, HurwitzZeta.hurwitzZeta_one_sub, PositiveLinearMap.ofPreGNS_toPreGNS, Complex.deriv_cos', Complex.imCLM_coe, WeakFEPair.hf_modif_FE, integral_gaussian_sq_complex, Complex.isQuotientMap_im, CStarMatrix.normedSpaceCore, circleAverage_log_norm_factorizedRational, Complex.ofReal_qsmul, MeasureTheory.charFunDual_prod', ContinuousLinearMap.isPositive_iff_complex, HurwitzZeta.hurwitzOddFEPair_gâ, ArithmeticFunction.LSeriesSummable_zeta_iff, SchwartzMap.toLp_fourierTransform_eq, fourierIntegral_half_period_translate, MeasureTheory.stronglyMeasurable_charFun, PeriodPair.instDiscreteTopologySubtypeComplexMemSubmoduleIntLattice, qExpansion_neg, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, Complex.one_cpow, Complex.sin_pi, ModularForm.const_apply, Complex.continuous_ofReal, Complex.ofReal_zsmul, NumberField.mixedEmbedding.logMap_apply, Complex.conj_ofNat, Orientation.kahler_map, Complex.exp_pi_mul_I, isBigO_deriv_ofReal_cpow_const_atTop, Complex.not_continuousAt_Gamma_neg_nat, TemperedDistribution.instFourierInvAdd, MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, Polynomial.C_eq_or_isOpenQuotientMap_eval, LSeries.mul_delta_eq_smul_delta, Complex.isPrimitiveRoot_exp_rat_of_odd_num, Complex.tan_add_int_mul_pi, hasDerivAt_ofReal_cpow_const, EisensteinSeries.summable_e2Summand_symmetricIcc, LSeriesSummable.sub, Complex.I_mul_I, Polynomial.leading_coeff_le_mahlerMeasure, UnitAddTorus.hasSum_prod_mFourierCoeff, NumberField.mixedEmbedding.latticeBasis_apply, Complex.isIntegral_two_mul_cos_rat_mul_pi, NumberField.mixedEmbedding.unit_smul_eq_zero, OnePoint.IsBoundedAt.add, Complex.selfAdjointEquiv_symm_apply, TemperedDistribution.fourierInv_apply, GaussianInt.re_toComplex, Complex.div_I, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Complex.ofRealHom_eq_coe, Complex.sin_eq_tsum, Complex.cpow_eq_pow, Complex.Gammaâ_one_sub_mul_Gammaâ_one_add, differentiableAt_jacobiThetaâ_snd, Complex.tan_add_nat_mul_pi, Complex.mem_slitPlane_iff, HurwitzZeta.hurwitzOddFEPair_f, fourierCoeff.const_mul, SchwartzMap.instFourierSMul, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, SchwartzMap.fourierTransformCLM_apply, NumberField.mixedEmbedding.measurable_polarCoord_symm, Complex.cpow_nat_mul', LSeries.tendsto_atTop, SlashInvariantForm.slash_S_apply, NumberField.mixedEmbedding.fundamentalCone.intNorm_coe, NumberField.mixedEmbedding.norm_eq_zero_iff, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, one_add_cpow_hasFPowerSeriesOnBall_zero, ModularForm.coe_intCast, Complex.exp_sub_pi_mul_I, SchwartzMap.fderivCLM_fourier_eq, ProbabilityTheory.iIndepFun_iff_charFun_pi, CStarModule.inner_mul_inner_swap_le, Complex.hasSum_conj', Complex.isOpen_im_lt_EReal, NumberField.norm_embedding_le_house, TemperedDistribution.instLineDerivAdd, Complex.norm_sub_eq_iff, Circle.coe_inv, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, Complex.finrank_real_complex, NumberField.canonicalEmbedding_injective, Polynomial.Chebyshev.complex_ofReal_eval_U, NumberField.InfinitePlace.LiesOver.mk_embedding_comp, NumberField.mixedEmbedding.normAtPlace_nonneg, ZMod.dft_const_mul, Complex.tan_eq_zero_iff, Complex.Gammaâ_add_two, Set.Countable.preimage_cexp, mellin_differentiableAt_of_isBigO_rpow_exp, Complex.measurable_sin, Complex.UnitDisc.coe_zero, Complex.GammaSeq_eq_approx_Gamma_integral, Complex.exp_conj, Complex.nnnorm_exp_ofReal_mul_I, LSeriesSummable.isBigO_rpow, LSeries_zero, VectorFourier.integral_bilin_fourierIntegral_eq_flip, Complex.exp_sub_sinh, unitary_iff_isStarNormal_and_spectrum_subset_unitary, Complex.finrank_real_complex_fact, CFC.monotone_sqrt, NumberField.mixedEmbedding.logMap_real, NumberField.mixedEmbedding.commMap_apply_of_isReal, MeasureTheory.Lp.inner_fourier_eq, AlgHom.map_coe_real_complex, cexp_neg_quadratic_isLittleO_rpow_atTop, NormedSpace.of_real_exp_â_â, Complex.cpow_ofReal_im, NumberField.mixedEmbedding.polarCoord_apply, TemperedDistribution.instLineDerivSMulComplex, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, LSeries_analyticOn, Complex.iteratedDeriv_odd_cos, Set.Countable.preimage_circleMap, ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet, Complex.sin_sub, Function.Complex.hasTemperateGrowth_ofReal, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, Polynomial.logMahlerMeasure_zero, Complex.cpow_add, Complex.ofReal_comp_nsmul, WeakFEPair.functional_equation, Complex.I_sq, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, Complex.equivRealProdCLM_symm_apply_re, UpperHalfPlane.sinh_half_dist_add_dist, Complex.norm_I, Complex.cos_eq, NumberField.mixedEmbedding.continuous_normAtAllPlaces, Polynomial.Chebyshev.U_complex_cos, Complex.ofReal_div, MeasureTheory.charFunDual_eq_pi_iff', IsCompact.reProdIm, ModularForm.coe_norm, Complex.sin_add_sin, Complex.sq_nonpos_iff, Complex.cpow_nat_inv_pow, Complex.ofReal_comp_zsmul, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, HurwitzZeta.differentiable_cosZeta_of_ne_zero, HurwitzZeta.sinZeta_neg, norm_cfcâ_one_sub_one_add_inv_lt_one, NumberField.mixedEmbedding.latticeBasis_repr_apply, Complex.dist_mk, ModularFormClass.qExpansion_isBigO, NumberField.canonicalEmbedding.apply_at, SchwartzMap.integral_fourierInv_mul_eq, Real.fourierIntegral_continuousLinearMap_apply', HurwitzZeta.completedCosZeta_eq, Complex.isCauSeq_im, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, ProbabilityTheory.complexMGF_id_gaussianReal, Complex.mul_conj, HurwitzZeta.completedCosZeta_one_sub, Complex.summable_one_div_nat_cpow, Complex.im_ofReal_mul, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, Complex.nndist_conj_comm, Complex.exp_rat_mul_pi_mul_I_pow_two_mul_den, VonNeumannAlgebra.coe_toStarSubalgebra, CuspForm.IsGLPos.smul_apply, rank_real_of_complex, Complex.differentiableAt_Gamma_one, Real.differentiable_fourierChar, ValueDistribution.proximity_pow_top, NumberField.AdeleRing.algebraMap_fst_apply, Complex.digamma_one, VectorFourier.fourierPowSMulRight_apply, skewAdjointPart_eq_I_smul_imaginaryPart, summable_prod_eisSummand, mdifferentiable_jacobiTheta, Complex.inv_im, jacobiTheta_eq_jacobiThetaâ, Polynomial.Chebyshev.C_two_mul_complex_cos, StarSubalgebra.coe_isUnit, Complex.exp_mem_slitPlane, Complex.conj_natCast, Complex.range_norm, polarCoord_apply, NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal, Complex.measurable_log, WithCStarModule.inner_single_left, PeriodPair.derivWeierstrassPExcept_neg, Complex.zero_re, Complex.instProperSpace, ModularForm.coe_add, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, Complex.cpow_int_mul', DirichletCharacter.not_LSeriesSummable_at_one, NumberField.mixedEmbedding.normAtPlace_negAt, Complex.nndist_conj_conj, SchwartzMap.convolution_flip, CuspForm.sub_apply, ModularFormClass.bdd_at_cusps, MeasureTheory.charFunDual_dirac, EisensteinSeries.G2_eq_tsum_cexp, Complex.isometryOfOrthonormal_apply, Cardinal.mk_complex, Complex.frontier_setOf_le_re_and_le_im, Complex.sameRay_iff, Complex.instContinuousMapUniqueHom, Circle.normSq_coe, PositiveLinearMap.leftMulMapPreGNS_mul_eq_comp, Complex.hasDerivAt_Gamma_one, NumberField.mixedEmbedding.normAtPlace_smul, PeriodPair.hasSum_weierstrassPExcept, ModularForm.coe_const, Complex.cpow_conj, Complex.compl_Iic_zero, completedRiemannZetaâ_one_sub, Complex.sin_mul_I, Complex.GammaSeq_mul, jacobiThetaâ'_undef, Complex.abs_re_lt_norm, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, NumberField.mixedEmbedding.finrank, SchwartzMap.integral_fourier_smul_eq, Function.Periodic.norm_qParam, Complex.imCLM_nnnorm, Complex.not_lt_zero_iff, GaussianInt.toComplex_zero, HurwitzZeta.hurwitzOddFEPair_k, Complex.sin_sub_pi, Complex.sin_add_mul_I, ModularForm.cuspFunction_mul, EisensteinSeries.qExpansion_identity, Complex.iteratedDeriv_even_sin, Complex.norm_exp_eq_iff_re_eq, UpperHalfPlane.contMDiffAt_ofComplex, fourierSubalgebra_closure_eq_top, ModularForm.prod_fintype_slash, GaussianFourier.integral_cexp_neg_sum_mul_add, selfAdjoint.val_re_map_spectrum, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Complex.IsExpCmpFilter.isLittleO_log_re_re, circleIntegrable_sub_inv_iff, RCLike.ofReal_eq_complex_ofReal, ModularFormClass.bounded_at_infty_comp_ofComplex, ArithmeticFunction.LSeriesHasSum_zeta, NumberField.mixedEmbedding.convexBodySum_isBounded, CuspFormClass.exp_decay_atImInfty', Complex.sameRay_iff_arg_div_eq_zero, Complex.arg_eq_nhds_of_im_pos, Complex.norm_cpow_inv_nat, ModularForm.holo', LSeries.abscissaOfAbsConv_sub_le, Complex.cos_pi_div_two_sub, NumberField.mixedEmbedding.polarSpaceCoord_apply, Real.nonempty_algEquiv_or, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, Complex.arg_real_mul, CuspForm.IsGLPos.coe_smul, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, ProbabilityTheory.analyticOn_complexMGF, Complex.ofReal_sub, rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val, Complex.integral_rpow_mul_exp_neg_mul_rpow, Complex.im_surjective, NumberField.mixedEmbedding.negAt_apply_norm_isReal, RCLike.im_to_complex, Complex.log_sub_logTaylor_isBigO, differentiable_completedZetaâ, Complex.angle_one_left, Complex.measurable_cosh, fourier_zero', SlashInvariantForm.vAdd_width_periodic, Complex.cosh_add, Complex.mul_inv_cancel, HurwitzZeta.hasSum_int_sinZeta, CFC.log_le_log, UpperHalfPlane.coe_vadd, Complex.differentiable_sinh, UpperHalfPlane.denom_one, AddChar.doubleDualEquiv_symm_doubleDualEmb_apply, Complex.UnitDisc.norm_lt_one, Complex.conj_eq_iff_real, Complex.re_surjective, Complex.iteratedDeriv_even_sinh, circleMap_zero_radius, ZMod.toCircle_intCast, Complex.toMatrix_conjAe, Complex.cos_sub_cos, ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log, ZMod.toCircle_natCast, inner_map_polarization, Complex.volume_ball, Real.deriv_fourierChar, RCLike.re_eq_complex_re, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, NumberField.InfinitePlace.embedding_injective, Real.iteratedFDeriv_fourierIntegral, cpow_eq_nhds', ModularFormClass.bdd_at_infty_slash, Complex.cos_eq_zero_iff_sin_eq, UpperHalfPlane.im_inv_neg_coe_pos, Complex.exp_eq_exp_re_mul_sin_add_cos, jacobiTheta_eq_tsum_nat, hasSum_sq_fourierCoeff, ModularFormClass.cuspFunction_apply_zero, Complex.canLift, PositiveLinearMap.norm_apply_le_of_nonneg, Complex.UnitDisc.instSMulCommClass_circle_closedBall, Complex.differentiable_iteratedDeriv_sinh, RCLike.norm_to_complex, Complex.isBigO_ofReal_right, LSeries.term_sum_apply, Function.Periodic.qParam_left_inv_mod_period, Complex.nnnorm_intCast, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, Complex.cpow_def, UpperHalfPlane.contMDiffAt_iff, Orientation.kahler_apply_apply, NonUnitalCStarAlgebra.toIsScalarTower, UpperHalfPlane.instIsManifoldComplexModelWithCornersSelfTopWithTopENat, Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSet, LSeries_eq_zero_of_abscissaOfAbsConv_eq_top, VonNeumannAlgebra.mem_commutant_iff, Complex.div_ofReal_im, UnitAddTorus.mFourierBasis_repr, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, Complex.differentiableAt_sinh, Complex.angle_one_right, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, Complex.cpow_mul_int, CuspFormClass.cuspFunction_apply_zero, hasDerivAt_ofReal_cpow_const', Complex.hasDerivAt_Gamma_one_half, Function.Periodic.differentiable_qParam, Complex.normSq_eq_conj_mul_self, ModularForm.slash_def, Complex.continuous_tan, Function.Periodic.contDiff_qParam, CFC.sqrt_le_sqrt, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Complex.lim_norm, PeriodPair.differentiableOn_weierstrassPExcept, ZMod.invDFT_def, Complex.re_zsmul, Real.differentiable_fourierChar_neg_bilinear_right, NumberField.InfinitePlace.mkComplex_coe, Complex.conjCLE_norm, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Complex.conj_eq_iff_im, fourierBasis_repr, differentiableAt_completedZeta, LSeries.delta_mul_eq_smul_delta, Complex.I_mul_im, Complex.tanh_zero, PeriodPair.derivWeierstrassPExcept_add_coe, Complex.isQuotientMap_re, Circle.coeHom_apply, Real.tendsto_integral_gaussian_smul, PeriodPair.derivWeierstrassPExcept_zero_zero, Complex.dist_conj_comm, CStarModule.continuous_inner, Complex.GammaIntegral_add_one, Complex.sin_neg, Complex.iteratedDeriv_add_one_cosh, Complex.sin_sub_int_mul_two_pi, rootsOfUnityCircleEquiv_apply, AddChar.FiniteField.primitiveChar_to_Complex_isPrimitive, CuspFormClass.zero_at_infty_slash, bernoulliFourierCoeff_recurrence, Complex.subfield_eq_of_closed, Complex.card_rootsOfUnity, Complex.exp_sub, VectorFourier.fourierIntegral_comp_add_right, PeriodPair.differentiableOn_weierstrassP, UnitAddTorus.span_mFourier_closure_eq_top, TemperedDistribution.laplacian_apply_apply, Complex.GammaIntegral_conj, ModularForm.is_invariant_one', Complex.imCLM_enorm, EisensteinSeries.eisensteinSeriesSIF_apply, Complex.Gamma_mul_Gamma_add_half, tendsto_integral_exp_inner_smul_cocompact, det_rotation, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, UpperHalfPlane.mdifferentiable_coe, WeakDual.Complex.instStarHomClass, Complex.cpow_inv_two_im_eq_neg_sqrt, Circle.coe_inj, Complex.cosh_neg, Complex.sin_two_pi_sub, Complex.arg_eq_nhds_of_re_pos, integral_complex_ofReal, imaginaryPart_smul, CliffordAlgebraComplex.toComplex_involute, NumberField.mixedEmbedding.norm_real, VectorFourier.fourierIntegral_probChar, SlashInvariantFormClass.norm_petersson_smul, continuousAt_jacobiThetaâ', Polynomial.logMahlerMeasure_const, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, NonUnitalCommCStarAlgebra.toSMulCommClass, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, EisensteinSeries.eisSummand_extension_differentiableOn, RCLike.to_complex_nonneg_iff, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Complex.arg_pow_coe_angle, integral_Ioi_cpow_of_lt, MeasureTheory.charFun_dirac, Fourier.fourierIntegral_def, CliffordAlgebraComplex.toComplex_ofComplex, Complex.isOpenQuotientMap_pow_compl_zero, HurwitzZeta.sinKernel_def, DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontal, ModularFormClass.analyticAt_cuspFunction_zero, Complex.cot_eq_exp_ratio, Complex.deriv_sinh, LSeries.pow_mul_term_eq, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, TemperedDistribution.lineDerivOp_apply_apply, Complex.HadamardThreeLines.diffContOnCl_invInterpStrip, MeasureTheory.ComplexMeasure.re_apply, Complex.rank_rat_complex, intervalIntegral.intervalIntegrable_cpow', Complex.deriv_sin, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Complex.norm_natCast_cpow_le_norm_natCast_cpow_iff, Complex.norm_natCast_cpow_le_norm_natCast_cpow_of_pos, Complex.exp_nat_mul, Complex.logTaylor_at_zero, Complex.norm_cpow_eq_rpow_re_of_nonneg, fourier_coe_apply', Complex.norm_exp_le_exp_norm, Complex.IsExpCmpFilter.isLittleO_cpow_exp, SlashInvariantForm.coe_add, NumberField.mixedEmbedding.polarSpaceCoord_source, cfc_real_eq_complex, ProbabilityTheory.complexMGF_undef, UnitAddTorus.hasSum_sq_mFourierCoeff, TemperedDistribution.lineDerivOp_fourierInv_eq, Complex.cos_sq, fourierCoeffOn_eq_integral, Complex.re_expect, HurwitzZeta.hurwitzOddFEPair_g, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, VonNeumannAlgebra.coe_commutant, UpperHalfPlane.dist_coe_le, spectrum.exists_nnnorm_eq_spectralRadius, PeriodPair.hasSum_sumInvPow, DirichletCharacter.LFunctionTrivChar_residue_one, Complex.hasDerivAt_tan, Complex.lintegral_comp_pi_polarCoord_symm, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, Complex.analyticWithinAt_sin, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, Complex.norm_exp_mul_exp_add_exp_neg_le_of_abs_im_le, Complex.exp_sum, rotation_symm, LSeriesHasSum.sum, ProbabilityTheory.IsGaussian.charFun_eq, CompletelyPositiveMap.map_cstarMatrix_nonneg', Complex.equivRealProdCLM_symm_apply_im, integral_gaussian_complex, circleMap_zero_pow, Complex.polarCoord_symm_apply, Complex.tan_sq_div_one_add_tan_sq, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, Complex.re_nnqsmul, summable_bernoulli_fourier, Real.fourier_continuousMultilinearMap_apply, ModularFormClass.differentiableOn_cuspFunction_ball, RCLike.im_eq_complex_im, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd, Polynomial.logMahlerMeasure_monomial, WeakFEPair.f_modif_aux1, ZMod.differentiable_completedLFunctionâ, CStarAlgebra.inr_mem_Icc_iff_nnnorm_le, Complex.ofReal_ratCast, Complex.IsExpCmpFilter.tendsto_abs_re, PeriodPair.periodic_weierstrassP, Complex.sin_zero, Complex.equiv_limAux, SchwartzMap.integral_inner_fourier_fourier, Complex.real_le_real, ModularFormClass.holo, ZMod.toCircle_apply, completedRiemannZeta_residue_one, NumberField.InfinitePlace.eq_iff_eq, unitary.norm_sub_one_lt_two_iff, EisensteinSeries.summable_e2Summand_symmetricIco, GaussianFourier.integrable_cexp_neg_sum_mul_add, HurwitzZeta.jacobiThetaâ''_conj, WithCStarModule.pi_norm_sq, EisensteinSeries.linear_isTheta_right, DirichletCharacter.delta_mul, AddChar.doubleDualEmb_inj, Complex.hasSum_sinh, NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, DirichletCharacter.rootNumber_modOne, integral_exp_mul_complex_Iic, circleIntegral.integral_sub_center_inv, Circle.arg_exp, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, Polynomial.logMahlerMeasure_C_mul_X_add_C, Complex.isAlgebraic_tan_rat_mul_pi, MeasureTheory.Lp.toTemperedDistribution_apply, TemperedDistribution.smulLeftCLM_const, Complex.norm_log_natCast_le_rpow_div, iteratedDeriv_cexp_const_mul, completedRiemannZeta_one, MeasureTheory.charFunDual_pi, SchwartzMap.fourier_fderivCLM_eq, Complex.range_exp, SchwartzMap.fourier_convolution_apply, Complex.Gammaâ_div_Gammaâ_one_sub, UpperHalfPlane.sinh_half_dist, Complex.differentiableAt_Gamma, Real.iteratedDeriv_fourierIntegral, Complex.adjoin_I, Complex.isIntegral_rat_I, HurwitzZeta.hurwitzZetaOdd_neg, LSeries.term_smul, Real.circleAverage_zero_one_congr_inv, UpperHalfPlane.dist_le_iff_le_sinh, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, EisensteinSeries.summable_right_one_div_linear_sub_one_div_linear_succ, HurwitzZeta.differentiableAt_cosZeta, Complex.hasSum_sin', jacobiThetaâ_fderiv_undef, Complex.cos_eq_neg_one_iff, Complex.logDeriv_cos, Complex.Gamma_mul_Gamma_one_sub, NumberField.mixedEmbedding.euclidean.finrank, Complex.arg_eq_nhds_of_re_neg_of_im_pos, Real.differentiable_fourierChar_neg_bilinear_left, DirichletCharacter.convolution_mul_moebius, EisensteinSeries.summable_linear_right_add_one_mul_linear_right, ModularForm.is_invariant_const, jacobiThetaâ_add_left, Complex.norm_prod, Complex.nnnorm_I, gelfandTransform_isometry, Quaternion.coe_ofComplex, Complex.log_neg_I, UpperHalfPlane.Ď_conj, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, fourierCoeff_liftIoc_eq, AddChar.doubleDualEmb_eq_zero, Complex.log_mul_ofReal, Complex.volume_sum_rpow_lt_one, circleIntegrable_log_norm_sub_const, Complex.betaIntegral_convergent_left, jacobiThetaâ_add_left', hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, TemperedDistribution.instContinuousFourierInv, Complex.cpow_int_mul, riemannZeta_neg_nat_eq_bernoulli', MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, Complex.re_add_im, Complex.nonneg_iff, Complex.sin_eq_tsum', mellin_differentiableAt_of_isBigO_rpow, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, Complex.reCLM_norm, Complex.im_eq_zero_iff_isSelfAdjoint, ModularForm.SL_slash_apply, UpperHalfPlane.dist_coe_center_sq, Complex.betaIntegral_eval_nat_add_one_right, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, Complex.conj_ofReal, VonNeumannAlgebra.instStarMemClass, ZMod.LFunction_residue_one, riemannZeta_def_of_ne_zero, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, NormedAlgebra.Complex.nonempty_algEquiv, NumberField.mixedEmbedding.convexBodySum_convex, PeriodPair.mul_Ďâ_add_mul_Ďâ_mem_lattice, Complex.normSq_apply, Complex.norm_exp_ofReal_mul_I, Complex.IsExpCmpFilter.eventually_ne, Circle.coe_exp, convex_halfSpace_im_le, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, Complex.real_lt_real, EisensteinSeries.eisSummand_SL2_apply, riemannZeta_eulerProduct_tprod, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne, Complex.arg_inv_coe_angle, Complex.exp_two_pi_mul_I, cpow_eq_nhds, UpperHalfPlane.tendsto_coe_atImInfty, TemperedDistribution.fourier_apply, NumberField.prod_archAbsVal_eq, Complex.isTheta_ofReal_left, NumberField.ComplexEmbedding.isReal_comp_iff, RCLike.normSq_to_complex, Complex.differentiable_cosh, Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, fourier_add', Complex.div_intCast_im, MeasureTheory.Integrable.fourier_smul, NumberField.ComplexEmbedding.IsConj.comp, Complex.frontier_setOf_le_re_and_im_le, hasMellin_cpow_Ioc, Complex.continuousAt_Gamma, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, tsum_sq_fourierCoeff, BoundedContinuousFunction.charMonoidHom_apply, Complex.sinh_sub, Complex.sin_surjective, Polynomial.cyclotomic_mahlerMeasure_eq_one, Complex.differentiable_iteratedDeriv_cos, Complex.sin_sq, SchwartzMap.coe_apply, integral_mul_cpow_one_add_sq, Complex.im_sq_le_normSq, Complex.IsExpCmpFilter.isLittleO_pow_mul_exp, CliffordAlgebraComplex.ofComplex_comp_toComplex, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, riemannZeta_residue_one, Complex.ofReal_tsum, realPart_smul, MeasureTheory.ComplexMeasure.equivSignedMeasureâ_apply, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, SlashInvariantForm.slash_action_eqn', AddChar.doubleDualEmb_doubleDualEquiv_symm_apply, Complex.norm_eq_sqrt_sq_add_sq, AddChar.coe_complexBasis, Polynomial.toAddCircle_X_eq_fourier_one, isTheta_deriv_ofReal_cpow_const_atTop, Complex.differentiable_cos, DirichletCharacter.isMultiplicative_zetaMul, SlashInvariantForm.coe_smul, Complex.neg_ofReal_mem_slitPlane, ModularForm.qExpansion_mul, GaussianFourier.verticalIntegral_norm_le, CircleIntegrable.out, VonNeumannAlgebra.instSubringClass, Complex.le_def, Complex.tan_mul_I, Complex.div_natCast, Real.circleAverage_add, LSeries_hasDerivAt, Complex.ofReal_comp_neg, CStarAlgebra.span_nonneg_inter_ball, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, Complex.isAlgClosed, Real.hasDerivAt_fourierIntegral, Complex.cos_nat_mul_two_pi_sub, Complex.conj_neg_I, UpperHalfPlane.mdifferentiableAt_iff, fourier_add_half_inv_index, Complex.natCast_arg, Complex.edist_of_re_eq, Complex.rightAngleRotation, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, PeriodPair.analyticOnNhd_weierstrassPExcept, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, integrable_cexp_quadratic, Complex.image_exp_Ioc_eq_sphere, CuspFormClass.exp_decay_atImInfty, Complex.measurable_ofReal, HurwitzZeta.completedHurwitzZetaEven_residue_zero, CircleIntegrable.abs, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, Complex.analyticAt_cos, UpperHalfPlane.denom_cocycle', Complex.analyticOnNhd_cos, Complex.ofRealAm_coe, deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, qExpansion_zero, HurwitzZeta.tendsto_hurwitzZeta_sub_one_div_nhds_one, Circle.toUnits_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, fourierCoeffOn.const_smul, CStarAlgebra.toStarModule, PeriodPair.indep, UpperHalfPlane.tanh_half_dist, Real.fourierInv_eq, jacobiThetaâ_add_right, Complex.inv_one_add_tan_sq, isConformalMap_complex_linear, ModularForm.coe_translate, Complex.exp_eq_one_iff, Complex.cos_nat_mul_two_pi_add_pi, SchwartzMap.tsum_eq_tsum_fourierIntegral, Complex.monotone_ofReal, Complex.inv_Gammaâ_one_sub, analyticWithinAt_cexp, Orientation.kahler_rightAngleRotation_right, Complex.cpow_mul_ofNat, ModularForm.coe_smul, Complex.norm_two, CFC.monotoneOn_cfcâ_rpowIntegrandââ, Complex.norm_cpow_le, MeasureTheory.intervalIntegrable_charFun, ModularForm.coe_sub, Complex.exp_mul_I_antiperiodic, Complex.arg_eq_nhds_of_re_neg_of_im_neg, Complex.isAbsoluteValueNorm, Complex.hasMeasurablePow, fourier_add, MeasureTheory.charFun_eq_integral_innerProbChar, Complex.re_nsmul, Complex.cpow_def_of_ne_zero, Complex.isLittleO_ofReal_right, LSeries.eq_zero_of_not_LSeriesSummable, Complex.exp_mul_I, DirichletCharacter.modZero_eq_delta, Complex.edist_of_im_eq, Complex.isAlgebraic_cos_rat_mul_pi, Complex.iteratedDeriv_odd_cosh, SchwartzMap.instFourierInvSMul, Complex.contDiff_sin, TemperedDistribution.derivCLM_apply_apply, Complex.hasDerivAt_exp, HurwitzZeta.hasSum_int_completedCosZeta, TorusIntegrable.function_integrable, DirichletCharacter.fourierTransform_eq_gaussSum_mulShift, Complex.contDiff_cos, Complex.hasSum_cosh, ModularForm.toFun_eq_coe, riemannZeta_neg_nat_eq_bernoulli, DirichletCharacter.LFunction_isBigO_horizontal, Complex.frontier_setOf_lt_re, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, SlashInvariantFormClass.petersson_smul, Complex.conj_tsum, Complex.isometryOfOrthonormal_symm_apply, Complex.arg_mul_cos_add_sin_mul_I_sub, UpperHalfPlane.Ď_mul_comm, SlashInvariantForm.neg_apply, NumberField.ComplexEmbedding.conjugate_coe_eq, IsStarNormal.instIsometricContinuousFunctionalCalculus, Complex.Gamma_ofNat_eq_factorial, Meromorphic.Gamma, Complex.intCast_im, ValueDistribution.proximity_coe, ModularForm.coe_trace, NumberField.ComplexEmbedding.lift_algebraMap_apply, integrable_mul_cexp_neg_mul_sq, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, Complex.frontier_setOf_le_im, Complex.GammaIntegral_convergent, HurwitzZeta.sinZeta_eq, Complex.cos_two_pi_sub, Polynomial.norm_coeff_le_choose_mul_mahlerMeasure, Complex.isOpenMap_exp, ZMod.dft_eq_fourier, Complex.ofReal_nnqsmul, ProbabilityTheory.IsGaussian.charFunDual_eq', convex_halfSpace_re_gt, Complex.enorm_exp_ofReal_mul_I, ZMod.dft_odd_iff, PeriodPair.weierstrassP_neg, AddChar.complexBasis_apply, Complex.one_re, ProbabilityTheory.analyticOnNhd_complexMGF, NumberField.mixedEmbedding.convexBodySum_volume, Complex.im_zsmul, riemannZeta_two_mul_nat, NumberField.mixedEmbedding.convexBodyLT'_neg_mem, Real.probChar_apply, UpperHalfPlane.range_coe, Complex.abs_cpow_inv_two_im, SlashInvariantForm.coe_const, CStarAlgebra.instNonnegSpectrumClassComplexUnital, Unitary.argSelfAdjoint_coe, Complex.ofReal_pow, UpperHalfPlane.im_pnat_div_pos, Polynomial.finite_mahlerMeasure_le, HurwitzZeta.completedHurwitzZetaOdd_one_sub, SlashInvariantForm.coeHom_injective, ModularForm.logDeriv_qParam, Complex.norm_le_sqrt_two_mul_max, skewAdjoint.I_smul_neg_I, Complex.tan_conj, tendsto_euler_sin_prod', EisensteinSeries.eisensteinSeries_slash_apply, Complex.coe_basisOneI, ProbabilityTheory.charFun_gaussianReal, WeakDual.CharacterSpace.exists_apply_eq_zero, Complex.polarCoord_target, SlashInvariantForm.coe_mul, Complex.map_isometryOfOrthonormal, DirichletCharacter.LSeriesSummable_zetaMul, Complex.arg_mul_coe_angle, TemperedDistribution.fourierTransformInv_apply, Circle.coe_injective, Complex.sin_sub_sin, Complex.hasSum_cos, Complex.logTaylor_succ, LinearMap.isSymmetric_iff_inner_map_self_real, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, HurwitzZeta.hurwitzZetaOdd_one_sub, ModularForm.coe_zero, UpperHalfPlane.contMDiff_smul, Complex.measurableEquivRealProd_symm_apply, Complex.isHomeomorphicTrivialFiberBundle_im, Quaternion.coeComplex_one, HurwitzZeta.hasSum_int_completedSinZeta, eqOn_iteratedDerivWithin_cotTerm_integerComplement, ProbabilityTheory.IndepFun.charFun_map_add_eq_mul, zeta_nat_eq_tsum_of_gt_one, spectrum.map_polynomial_aeval, Real.fourierInv_eq', UpperHalfPlane.tendsto_comap_im_ofComplex, Circle.coe_zpow, Complex.sinh_mul_I, MellinConvergent.cpow_smul, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, Real.fourierIntegral_deriv, jacobiThetaâ'_add_left, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, AddChar.expect_apply_eq_ite, Complex.reCLM_enorm, Complex.re_eq_norm, UpperHalfPlane.contMDiff_denom, Complex.norm_exp_I_mul_ofReal, Complex.tan_periodic, Complex.nnnorm_real, Polynomial.toAddCircle_C_eq_smul_fourier_zero, riemannZeta_eulerProduct_hasProd, torusMap_sub_center, Complex.isCauSeq_exp, MeasureTheory.norm_charFun_le, VectorFourier.hasFDerivAt_fourierChar_smul, BoundedContinuousFunction.separatesPoints_charPoly, DirichletCharacter.LSeries_eulerProduct, integrable_cexp_quadratic', Complex.sin_add_nat_mul_two_pi, Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, Real.fourierIntegral_real_eq, Complex.norm_intCast, NumberField.mixedEmbedding.logMap_zero, PeriodPair.lattice_eq_span_range_basis, MeasureTheory.measurable_charFun, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, CStarAlgebra.exists_sum_four_unitary, Complex.UnitDisc.coe_star, Complex.frontier_reProdIm, Polynomial.Gal.splits_â_â, Complex.cpow_zero, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, RCLike.re_to_complex, Complex.norm_cpow_eq_rpow_re_of_pos, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, Complex.norm_mul, ZMod.injective_stdAddChar, qExpansion_of_pow, Complex.exp_mul_I_periodic, Complex.re_sum, PeriodPair.Ďâ_mem_lattice, Complex.log_zero, SchwartzMap.fourier_convolution, OnePoint.isZeroAt_iff, ModularForm.add_apply, UnitAddTorus.span_mFourierLp_closure_eq_top, Complex.cpow_ofNat_inv_pow, Complex.zero_notMem_slitPlane, Complex.Gamma_eq_zero_iff, PeriodPair.analyticOnNhd_weierstrassP, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, NumberField.mixedEmbedding.normAtComplexPlaces_apply_isComplex, qExpansion_smul, Complex.differentiableAt_cos, WeakFEPair.f_modif_aux2, cfcHom_eq_of_isStarNormal, AddChar.zmodAddEquiv_apply, UpperHalfPlane.mdifferentiable_denom_zpow, NumberField.InfinitePlace.card_complex_embeddings, Complex.upperHalfPlane_inter_integerComplement, mellin_cpow_smul, Complex.betaIntegral_eq_Gamma_mul_div, Complex.ofReal_inv, Complex.cos_eq_cos_iff, ZMod.dft_const_smul, MeromorphicOn.Gamma, Complex.cos_sq', Complex.frontier_setOf_im_le, Complex.integral_cpow_mul_exp_neg_mul_Ioi, NumberField.Units.complexEmbedding_inj, Complex.range_exp_mul_I, Complex.range_im, Complex.mem_reProdIm, Circle.coe_div, Complex.dist_of_re_eq, Complex.isUniformEmbedding_equivRealProd, MeasureTheory.charFun_map_const_add, NumberField.mixedEmbedding.fundamentalCone.measurableSet_normLeOne, Complex.normSq_neg, MeasureTheory.charFun_eq_pi_iff, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, SlashInvariantFormClass.slash_action_eq, integral_cos_mul_complex, Complex.IsExpCmpFilter.isLittleO_cpow_mul_exp, Circle.coe_one, ModularForm.summable_eta_q, Polynomial.fourierCoeff_toAddCircle, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, ZMod.dft_smul_const, Complex.hasSum_iff, Complex.exp_multiset_sum, NumberField.mixedEmbedding.norm_negAt, HurwitzZeta.differentiable_completedHurwitzZetaEvenâ, ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAux, SlashInvariantForm.slash_action_eqn, NumberField.mixedEmbedding.norm_unit, ZMod.completedLFunction_modOne_eq, VectorFourier.fourierIntegral_fderiv, HurwitzZeta.differentiable_completedHurwitzZetaOdd, summable_pow_mul_cexp, HurwitzZeta.sinZeta_one_sub, Complex.cpow_ofNat, WeakFEPair.Î_residue_zero, ModularFormClass.hasSum_qExpansion, Complex.Gamma_zero, HurwitzZeta.completedHurwitzZetaEvenâ_one_sub, BoundedContinuousFunction.char_add_eq_mul, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, Real.fourierIntegralInv_eq, Complex.isOpenMap_re, WithCStarModule.prod_inner, Complex.approx_Gamma_integral_tendsto_Gamma_integral, Complex.cpow_two, MeasureTheory.Lp.fourier_toTemperedDistribution_eq, Complex.log_conj, Complex.isSquare, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, Complex.smul_im, Complex.IsExpCmpFilter.isTheta_cpow_exp_re_mul_log, CircleIntegrable.finsum, MeasureTheory.charFun_prod, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, Complex.inv_Gammaâ_two_sub, SchwartzMap.toLp_fourier_eq, UpperHalfPlane.continuous_coe, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Complex.deriv_exp, Complex.isIntegral_int_I, Real.fderiv_fourierChar_neg_bilinear_left_apply, Complex.add_intCast_mem_integerComplement, isConformalMap_iff_is_complex_or_conj_linear, ZMod.dft_def, Complex.Gamma_one_half_eq, PeriodPair.Ďâ_mem_lattice, DirichletCharacter.differentiable_LFunctionTrivCharâ, summable_jacobiThetaâ'_term_iff, Real.fourierIntegral_continuousMultilinearMap_apply', Complex.range_normSq, LSeriesHasSum.neg, ValueDistribution.proximity_top, NumberField.InfinitePlace.apply, Complex.integerComplement.mem_iff, Polynomial.mahlerMeasure_le_sum_norm_coeff, Real.fourier_eq', MeasureTheory.charFunDual_eq_prod_iff', EisensteinSeries.summand_bound, Complex.cosh_mul_I, UpperHalfPlane.mdifferentiable_iff, Real.fourierIntegral_iteratedFDeriv, Complex.isOpen_re_gt_EReal, ModularFormClass.exp_decay_sub_atImInfty', Complex.neg_re_eq_norm, Complex.cos_int_mul_two_pi, UpperHalfPlane.smulAux'_im, NonUnitalCStarAlgebra.toSMulCommClass, Complex.one_mem_slitPlane, Complex.arg_neg_eq_arg_sub_pi_iff, WeakFEPair.Î_residue_k, integrable_cexp_neg_mul_sq, Complex.sq_cpow_two_inv, Complex.analyticAt_iff_eventually_differentiableAt, Complex.cos_two_pi, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, Fourier.fourierIntegral_comp_add_right, Complex.cos_add_int_mul_two_pi, Complex.mul_I_im, CircleIntegrable.add, UpperHalfPlane.isOpen_upperHalfPlaneSet, Complex.conj_I, continuousFunctionalCalculus_map_id, UpperHalfPlane.isEmbedding_coe, Complex.isCauSeq_re, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, HurwitzZeta.differentiable_completedSinZeta, HurwitzZeta.differentiable_hurwitzZetaEven_sub_hurwitzZetaEven, CFC.conjugate_rpow_neg_one_half, Complex.tan_inv_eq_cot, Real.rpow_def, Complex.analyticOnNhd_sinh, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, Complex.analyticWithinAt_cos, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, SlashInvariantForm.vAdd_apply_of_mem_strictPeriods, Complex.imLm_coe, Complex.stolzSet_empty, Complex.normSq_ofReal_sub_I_mul_sqrt_one_sub, Complex.mem_slitPlane_or_neg_mem_slitPlane, NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm, ModularForm.is_invariant_one, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, Complex.exp_int_mul, Complex.arg_zpow_coe_angle, ModularForm.mul_coe, PeriodPair.derivWeierstrassPExcept_def, EisensteinSeries.D2_T, Complex.exp_int_mul_two_pi_mul_I, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, Complex.div_natCast_re, Complex.continuousAt_ofReal_cpow_const, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, circleMap_mem_sphere', Complex.neg_im, GaussianInt.toComplex_one, Circle.argEquiv_apply_coe, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, NumberField.InfinitePlace.comap_embedding_of_isReal, LSeries.hasDerivAt_term, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, Complex.re_nnratCast, UpperHalfPlane.mdifferentiableAt_ofComplex, integrableOn_Ioi_deriv_norm_ofReal_cpow, Complex.normSq_eq_zero, CStarAlgebra.span_unitary, ContinuousLinearMap.circleAverage_comp_comm, Complex.isLittleO_ofReal_left, Complex.mem_slitPlane_iff_not_le_zero, Complex.log_exp_exists, Summable.hasSumUniformlyOn_log_one_add, CFC.complex_exp_eq_normedSpace_exp, Complex.horizontalSegment_eq, SlashInvariantForm.coe_norm, Complex.ofReal_mul, fourier_gaussian_pi, le_iff_norm_sqrt_mul_rpow, Complex.sin_arg, UpperHalfPlane.Ď_denom, Complex.det_conjLIE, Complex.sinh_sub_cosh, NumberField.house.basis_repr_norm_le_const_mul_house, Complex.dist_conj_self, WeakFEPair.differentiable_Îâ, EisensteinSeries.D2_mul, TemperedDistribution.laplacianCLM_apply, completedRiemannZeta_one_sub, continuousAt_gaussian_integral, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Complex.div_ratCast, torusIntegral_succAbove, coeFn_fourierLp, Real.deriv_fourier, CStarAlgebra.exists_sum_four_nonneg, fourierCoeff_liftIco_eq, CuspForm.coe_add, CuspForm.toSlashInvariantForm_coe, NumberField.mixedEmbedding.disjoint_negAt_plusPart, Complex.UnitDisc.coe_circle_smul, GaussianInt.normSq_div_sub_div_lt_one, CuspForm.smul_apply, ZMod.stdAddChar_apply, DirichletCharacter.continuousOn_neg_logDeriv_LFunctionTrivCharâ, Complex.cos_arg, DirichletCharacter.differentiable_completedLFunction, Complex.continuousAt_tan, NumberField.mixedEmbedding.logMap_mul, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, PositiveLinearMap.preGNS_norm_sq, EulerSine.integral_cos_mul_cos_pow_even, circleIntegral.integral_const_mul, HurwitzZeta.differentiableAt_expZeta, Complex.cosh_sub_sinh, Polynomial.card_mahlerMeasure_le_prod, NumberField.house_eq_sup', Complex.norm_natCast_cpow_of_re_ne_zero, SlashInvariantForm.coe_intCast, Complex.cpow_ne_zero_iff, GaussianInt.intCast_complex_norm, Complex.Gammaâ_one, Complex.nonempty_linearEquiv_real, LSeries_convolution, Complex.continuous_im, WeakDual.CharacterSpace.instStarHomClass, GaussianInt.intCast_re, Complex.coe_reAddGroupHom, Complex.ofReal_choose, NonUnitalCommCStarAlgebra.toIsScalarTower, Complex.equivRealProdCLM_apply, Circle.argPartialEquiv_apply, Complex.logDeriv_cosh, MeasureTheory.charFun_eq_integral_probChar, NumberField.mixedEmbedding.convexBodySum_mem, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Complex.instCharZero, Complex.cos_pi, ModularGroup.smul_eq_lcRow0_add, Complex.Gammaâ_mul_Gammaâ_add_one, fourierIntegral_gaussian_pi', PeriodPair.finrank_lattice, PeriodPair.derivWeierstrassP_add_coe, Unitization.inr_nonneg_iff, RCLike.I_to_complex, Complex.rank_real_complex, Complex.orderClosedTopology, CStarMatrix.norm_def, HurwitzZeta.differentiableAt_sinZeta, ModularForm.multipliableLocallyUniformlyOn_eta, Complex.tan_two_mul, HurwitzZeta.hurwitzZetaEven_eq, integral_gaussian_complex_Ioi, ModularForm.constâ_toFun, ModularForm.SL_smul_slash, PeriodPair.derivWeierstrassP_zero, Complex.isEquivalent_sin, NumberField.mixedEmbedding.convexBodyLT'_convex, selfAdjoint.expUnitary_coe, MeasureTheory.charFun_map_add_const, Complex.abs_re_div_norm_le_one, TemperedDistribution.smulLeftCLM_apply_apply, Complex.not_lt_iff, summable_jacobiThetaâ_term_iff, Complex.UnitDisc.sq_norm_lt_one, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, Circle.norm_smul, Complex.arg_eq_pi_iff_lt_zero, LSeries.term_zero, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly, NumberField.mixedEmbedding.norm_apply, mellin_comp_mul_left, jacobiTheta_two_add, Complex.cpow_ofReal, GaussianInt.toComplex_div_im, Complex.equivRealProd_apply_le, BoundedContinuousFunction.char_mem_charPoly, MeasureTheory.SignedMeasure.im_toComplexMeasure, Complex.sin_add_pi, differentiableAt_jacobiTheta, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, Complex.lim_re, Complex.rotation, ZMod.dft_apply_zero, Complex.two_sin, RCLike.complexLinearIsometryEquiv_apply, pi_mul_cot_pi_q_exp, Complex.one_im, Complex.cosh_add_sinh, BoundedContinuousFunction.probCharDual_apply, PeriodPair.weierstrassPExcept_add, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, Complex.hasDerivAt_Gamma_nat, IsClosed.reProdIm, Complex.cos_sub_int_mul_two_pi, CStarMatrix.inner_toCLM_conjTranspose_right, norm_jacobiThetaâ_term_fderiv_le, SlashInvariantForm.T_zpow_width_invariant, Complex.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, GaussianInt.toComplex_eq_zero, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, Complex.isometry_intCast, Complex.normSq_one, Complex.sin_add_pi_div_two, Complex.sqrt_one, PeriodPair.instIsZLatticeRealComplexLattice, mellin_comp_mul_right, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, Summable.tendstoUniformlyOn_tsum_nat_log_one_add, NumberField.mixedEmbedding.normAtPlace_real, EisensteinSeries.linear_inv_isBigO_right, CStarMatrix.toCLM_apply_single_apply, BoundedContinuousFunction.char_apply, Complex.norm_mul_sin_arg, Complex.tendsto_exp_comap_re_atBot_nhdsNE, differentiable_circleMap, map_isSelfAdjoint, Complex.arg_neg_coe_angle, UpperHalfPlane.mdifferentiable_smul, Complex.dist_eq_re_im, ModularForm.slash_apply, HurwitzZeta.tendsto_hurwitzZetaEven_sub_one_div_nhds_one, Complex.lt_def, integrableOn_exp_mul_complex_Ioi, Complex.angle_exp_exp, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, Complex.isClosed_range_intCast, ArithmeticFunction.abscissaOfAbsConv_moebius, ProbabilityTheory.indepFun_iff_charFunDual_prod, le_iff_norm_sqrt_mul_sqrt_inv, Complex.two_cos, HurwitzZeta.differentiable_completedCosZetaâ, Complex.countable_preimage_exp, Complex.restrictScalars_toSpanSingleton', circleMap_zero_zpow, Complex.re_ofReal_mul, Complex.lim_eq_lim_im_add_lim_re, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, LSeries.norm_term_le_of_re_le_re, Complex.differentiable_iteratedDeriv_cosh, MeasureTheory.charFunDual_conv, Complex.closedEmbedding_intCast, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, HurwitzZeta.hurwitzZetaEven_residue_one, analyticAt_cexp, NumberField.mixedEmbedding.convexBodySumFun_eq_zero_iff, EisensteinSeries.G2_T_transform, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, Complex.reCLM_apply, CuspForm.add_apply, Complex.closure_setOf_im_lt, NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm, PeriodPair.differentiableOn_derivWeierstrassPExcept, Complex.conjLIE_symm, UpperHalfPlane.petersson_slash, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, fourierCoeff_fourier, ModularGroup.coe_truncatedFundamentalDomain, Polynomial.int_cyclotomic_spec, LSeriesSummable.neg
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