Theorems · Theorem · complex analysis
Function.Periodic.cuspFunction_zero_of_zero_at_inf
∀ {h : ℝ} {f : ℂ → ℂ},
0 < h → (Filter.comap Complex.im Filter.atTop).ZeroAtFilter f → Function.Periodic.cuspFunction h f 0 = 0- Defined in
- Mathlib.Analysis.Complex.Periodic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Compl.complproof · cited by 2,925
- Filter.atTopstatement and proof · cited by 2,405
- nhdsWithinproof · cited by 1,912
- Complex.imstatement and proof · cited by 591
- Filter.Tendsto.compproof · cited by 560
- Filter.comapstatement and proof · cited by 546
- Function.update_selfproof · cited by 201
- Filter.limUnderproof · cited by 47
- Filter.Tendsto.limUnder_eqproof · cited by 19
- Function.Periodic.invQParamproof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- UpperHalfPlane.IsZeroAtImInfty.cuspFunction_apply_zeroproof · cited by 1
- ModularForm.discriminant_cuspFunction_eqOnproof · cited by 1
- Function.Periodic.exp_decay_of_zero_at_infproof · cited by 0