Theorems · Theorem · number theory

UpperHalfPlane.qExpansion_coeff_zero

∀ {h : ℝ} {f : UpperHalfPlane → ℂ},
  0 < h →
    AnalyticAt ℂ (UpperHalfPlane.cuspFunction h f) 0 →
      Function.Periodic (f ∘ ↑UpperHalfPlane.ofComplex) ↑h →
        (PowerSeries.coeff 0) (UpperHalfPlane.qExpansion h f) = UpperHalfPlane.valueAtInfty f

Defined in: Mathlib.NumberTheory.ModularForms.QExpansion
Cited by: 2 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites22

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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PowerSeries.coeffstatement · cited by 324

Cited by2

Results whose statement or proof uses this declaration.

ModularForm.isCuspForm_iff_coeffZero_eq_zeroproof · cited by 2
ModularForm.isZeroAt_of_coeffZero_eq_zeroproof · cited by 1