Theorems · Theorem · number theory
UpperHalfPlane.IsZeroAtImInfty.zero_at_infty_comp_ofComplex
∀ {f : UpperHalfPlane → ℂ},
UpperHalfPlane.IsZeroAtImInfty f → (Filter.comap Complex.im Filter.atTop).ZeroAtFilter (f ∘ ↑UpperHalfPlane.ofComplex)- Cited by
- 2 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Filter.atTopstatement · cited by 2,405
- OpenPartialHomeomorph.toFun'statement · cited by 745
- UpperHalfPlanestatement and proof · cited by 626
- Complex.imstatement · cited by 591
- Filter.Tendsto.compproof · cited by 560
- Filter.comapstatement · cited by 546
- UpperHalfPlane.ofComplexstatement · cited by 59
- UpperHalfPlane.IsZeroAtImInftystatement and proof · cited by 24
- Filter.ZeroAtFilterstatement · cited by 11
- UpperHalfPlane.tendsto_comap_im_ofComplexproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- UpperHalfPlane.IsZeroAtImInfty.cuspFunction_apply_zeroproof · cited by 1
- ModularForm.discriminant_cuspFunction_eqOnproof · cited by 1