Theorems · Theorem · number theory

UpperHalfPlane.qExpansion_coeff_unique

∀ {F : Type u_1} [inst : FunLike F UpperHalfPlane ℂ] {h : ℝ} (f : F) {c : ℕ → ℂ},
  0 < h →
    AnalyticAt ℂ (UpperHalfPlane.cuspFunction h ⇑f) 0 →
      (∀ (τ : UpperHalfPlane), HasSum (fun m => c m • Function.Periodic.qParam h ↑τ ^ m) (f τ)) →
        ∀ (m : ℕ), c m = (PowerSeries.coeff m) (UpperHalfPlane.qExpansion h ⇑f)

Defined in

Mathlib.NumberTheory.ModularForms.QExpansion

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FunLike