Theorems · Definition · number theory
CuspForm.mulModularForm
{Γ : Subgroup (GL (Fin 2) ℝ)} →
[Γ.HasDetPlusMinusOne] → {k₁ k₂ : ℤ} → CuspForm Γ k₁ → ModularForm Γ k₂ → CuspForm Γ (k₁ + k₂)Multiplying a CuspForm by a ModularForm gives a CuspForm (the cusp condition is
preserved since a function tending to zero times a bounded function tends to zero).
- Defined in
- Mathlib.NumberTheory.ModularForms.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subgroup.HasDetPlusMinusOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- OnePointproof · cited by 126
- OnePoint.inftyproof · cited by 102
- ModularFormstatement and proof · cited by 98
- Subgroup.HasDetPlusMinusOnestatement and proof · cited by 57
- IsCuspproof · cited by 51
- SlashInvariantFormproof · cited by 46
- CuspFormstatement and proof · cited by 36
- ModularForm.toSlashInvariantFormproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- CuspForm.ofMulDiscriminantproof · cited by 1
- CuspForm.coe_mulModularFormstatement and proof · cited by 0