Mathlib Map

Theorems · Theorem · complex analysis

norm_circleMap_zero

∀ (R θ : ℝ), ‖circleMap 0 R θ‖ = |R|
Defined in
Mathlib.Analysis.SpecialFunctions.Complex.CircleMap
Cited by
21 results in Mathlib
Foundations
Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

circleMap_mem_sphere' · cited by 14circleMap_mem_sphere'MeromorphicOn.circleIntegrable_log_norm · cited by 11MeromorphicOn.circleInteg…CircleIntegrable.out · cited by 5CircleIntegrable.outReal.circleAverage_mono · cited by 3Real.circleAverage_monoReal.ContinuousOn.circleAverage · cited by 2ContinuousOn.circleAveragecircleIntegrable_iff · cited by 2circleIntegrable_iffhasSum_two_pi_I_cauchyPowerSeries_integral · cited by 2hasSum_two_pi_I_cauchyPow…circleAverage_log_norm_sub_const₁ · cited by 1circleAverage_log_norm_su…ValueDistribution.Cartan.integrable_integral_norm_cartanKernel · cited by 1Cartan.integrable_integra…hasDerivAt_circleAverage_herglotzRieszKernel_smul · cited by 1hasDerivAt_circleAverage_…norm_cauchyPowerSeries_le · cited by 1norm_cauchyPowerSeries_lecircleIntegral.norm_integral_le_of_norm_le_const' · cited by 1circleIntegral.norm_integ…circleIntegral.norm_integral_lt_of_norm_le_const_of_lt · cited by 1circleIntegral.norm_integ…circleMap_notMem_ball · cited by 1circleMap_notMem_ballPolynomial.mahlerMeasure_le_sum_norm_coeff · cited by 1Polynomial.mahlerMeasure_…Real · cited by 25697RealComplex · cited by 5565ComplexNorm.norm · cited by 5413Norm.normmul_one · cited by 3885mul_onezero_add · cited by 2366zero_addabs · cited by 1814absComplex.ofReal · cited by 1654Complex.ofRealComplex.I · cited by 866Complex.IComplex.exp · cited by 612Complex.expcircleMap · cited by 117circleMapComplex.norm_real · cited by 105Complex.norm_realComplex.norm_mul · cited by 59Complex.norm_mulComplex.norm_exp_ofReal_mul_I · cited by 14Complex.norm_exp_ofReal_m…norm_circleMap_zeroCITED BYCITES

Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.