Theorems · Theorem · number theory

ModularForm.isZeroAtImInfty_of_valueAtInfty_eq_zero

∀ {Γ : Subgroup (GL (Fin 2) ℝ)} {k : ℤ} {F : Type u_1} [inst : FunLike F UpperHalfPlane ℂ] [DiscreteTopology ↥Γ]
  [Γ.HasDetPlusMinusOne] [Fact (IsCusp OnePoint.infty Γ)] [ModularFormClass F Γ k] (f : F),
  UpperHalfPlane.valueAtInfty ⇑f = 0 → UpperHalfPlane.IsZeroAtImInfty ⇑f

A modular form with valueAtInfty f = 0 is zero at infinity.

Defined in: Mathlib.NumberTheory.ModularForms.CuspFormSubmodule
Cited by: 1 results in Mathlib
Foundations: Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: FunLike DiscreteTopology Subgroup.HasDetPlusMinusOne Fact ModularFormClass

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Cited by1

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ModularForm.isZeroAt_of_coeffZero_eq_zeroproof · cited by 1