Theorems · Theorem · number theory
UpperHalfPlane.qExpansion_smul
∀ {h : ℝ} {f : UpperHalfPlane → ℂ},
AnalyticAt ℂ (UpperHalfPlane.cuspFunction h f) 0 →
∀ (a : ℂ), UpperHalfPlane.qExpansion h (a • f) = a • UpperHalfPlane.qExpansion h f- Cited by
- 2 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.
Cites17
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
- PowerSeriesstatement · cited by 797
- UpperHalfPlanestatement and proof · cited by 626
- Nat.factorialproof · cited by 616
- map_smulproof · cited by 566
- PowerSeries.coeffproof · cited by 324
- AnalyticAtstatement and proof · cited by 321
- iteratedDerivproof · cited by 188
- mul_left_commproof · cited by 184
- PowerSeries.extproof · cited by 69
- UpperHalfPlane.qExpansionstatement and proof · cited by 64
Cited by2
Results whose statement or proof uses this declaration.
- ModularForm.qExpansion_smulproof · cited by 4
- UpperHalfPlane.qExpansion_negproof · cited by 2