Theorems · Theorem · number theory

UpperHalfPlane.hasFPowerSeries_cuspFunction

∀ {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)) →
        HasFPowerSeriesOnBall (UpperHalfPlane.cuspFunction h ⇑f) (UpperHalfPlane.qExpansionFormalMultilinearSeries h f)
          0 1

The q-expansion of f is an FPowerSeries representing cuspFunction n f.

Defined in

Mathlib.NumberTheory.ModularForms.QExpansion

Cited by

1 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FunLike