Theorems · Theorem · complex analysis
Function.Periodic.norm_qParam_lt_iff
∀ {h : ℝ}, 0 < h → ∀ (A : ℝ) (z : ℂ), ‖Function.Periodic.qParam h z‖ < Real.exp (-2 * Real.pi * A / h) ↔ A < z.im- Defined in
- Mathlib.Analysis.Complex.Periodic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Real.pistatement and proof · cited by 1,774
- Real.expstatement and proof · cited by 871
- neg_mulproof · cited by 654
- Complex.imstatement and proof · cited by 591
- Real.pi_posproof · cited by 173
- Function.Periodic.qParamstatement · cited by 42
- div_lt_div_iff_of_pos_rightproof · cited by 15
- Real.exp_lt_expproof · cited by 11
- Function.Periodic.norm_qParamproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Function.Periodic.norm_qParam_lt_oneproof · cited by 2