Theorems · Theorem · number theory
UpperHalfPlane.qExpansion_eq_zero_iff
∀ {h : ℝ} {f : UpperHalfPlane → ℂ},
0 < h →
Function.Periodic (f ∘ ↑UpperHalfPlane.ofComplex) ↑h →
MDiff f → UpperHalfPlane.IsBoundedAtImInfty f → (UpperHalfPlane.qExpansion h f = 0 ↔ f = 0)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- SummationFilter.unconditionalproof · cited by 2,068
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- tsumproof · cited by 1,148
- modelWithCornersSelfstatement and proof · cited by 920
- PowerSeriesstatement · cited by 797
- OpenPartialHomeomorph.toFun'statement and proof · cited by 745
- UpperHalfPlanestatement and proof · cited by 626
Cited by1
Results whose statement or proof uses this declaration.
- ModularForm.qExpansion_eq_zero_iffproof · cited by 1