Theorems · Theorem · number theory
ModularForm.isCuspForm_iff
∀ {Γ : Subgroup (GL (Fin 2) ℝ)} {k : ℤ} [inst : Γ.HasDetOne] (f : ModularForm Γ k),
f.IsCuspForm ↔ ∀ {c : OnePoint ℝ}, IsCusp c Γ → c.IsZeroAt (⇑f) kA modular form is a cusp form if and only if it vanishes at every cusp. This is the general characterization valid for any subgroup.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subgroup.HasDetOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- UpperHalfPlanestatement · cited by 626
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- OnePointstatement and proof · cited by 126
- ModularFormstatement and proof · cited by 98
- IsCuspstatement and proof · cited by 51
- CuspFormproof · cited by 36
- Subgroup.HasDetOnestatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- ModularForm.isCuspForm_iff_coeffZero_eq_zeroproof · cited by 2