Theorems · Theorem · number theory
EisensteinSeries.eisSummand_extension_differentiableOn
∀ (k : ℤ) (a : Fin 2 → ℤ),
DifferentiableOn ℂ (EisensteinSeries.eisSummand k a ∘ ↑UpperHalfPlane.ofComplex) {z | 0 < z.im}Auxiliary lemma showing that for any k : ℤ and (a : Fin 2 → ℤ)
the extension of eisSummand is differentiable on {z : ℂ | 0 < z.im}.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 194 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 · cited by 25,697
- Set.ofPredstatement and proof · cited by 6,101
- Complexstatement and proof · cited by 5,565
- OpenPartialHomeomorph.toFun'statement · cited by 745
- UpperHalfPlanestatement and proof · cited by 626
- Complex.imstatement and proof · cited by 591
- DifferentiableOnstatement · cited by 419
- UpperHalfPlane.coeproof · cited by 288
- UpperHalfPlane.ofComplexstatement · cited by 59
- EisensteinSeries.eisSummandstatement and proof · cited by 15
- DifferentiableOn.congrproof · cited by 10
- UpperHalfPlane.comp_ofComplexproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.eisensteinSeriesSIF_mdifferentiableproof · cited by 1