Theorems · Theorem · complex analysis
Function.Periodic.norm_qParam
∀ (h : ℝ) (z : ℂ), ‖Function.Periodic.qParam h z‖ = Real.exp (-2 * Real.pi * z.im / h)
- Defined in
- Mathlib.Analysis.Complex.Periodic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
- sub_zeroproof · cited by 938
- Complex.reproof · cited by 882
Cited by6
Results whose statement or proof uses this declaration.
- UpperHalfPlane.norm_exp_two_pi_I_lt_oneproof · cited by 7
- UpperHalfPlane.norm_qParam_lt_oneproof · cited by 5
- Function.Periodic.qParam_tendstoproof · cited by 3
- Function.Periodic.exp_decay_sub_of_bounded_at_infproof · cited by 2
- qExpansion_coeff_isBigO_of_norm_isBigOproof · cited by 2
- Function.Periodic.norm_qParam_lt_iffproof · cited by 1