Theorems · Theorem · number theory
CuspFormClass.qExpansion_coeff_zero
∀ {k : ℤ} {F : Type u_1} [inst : FunLike F UpperHalfPlane ℂ] {Γ : Subgroup (GL (Fin 2) ℝ)} {h : ℝ} (f : F)
[CuspFormClass F Γ k], 0 < h → h ∈ Γ.strictPeriods → (PowerSeries.coeff 0) (UpperHalfPlane.qExpansion h ⇑f) = 0The zeroth coefficient of the q-expansion of a cusp form vanishes.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FunLikeCuspFormClass
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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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- MulZeroClass.mul_zeroproof · cited by 2,091
- PowerSeriesstatement · cited by 797
Cited by1
Results whose statement or proof uses this declaration.
- ModularForm.discriminant_qExpansion_orderproof · cited by 1