Theorems · Theorem · number theory
Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z
∀ (𝒢 : Subgroup (GL (Fin 2) ℝ)) [𝒢.IsArithmetic] {c : OnePoint ℝ},
IsCusp c 𝒢 ↔ IsCusp c (Matrix.SpecialLinearGroup.mapGL ℝ).rangeThe cusps of any arithmetic subgroup are the same as those of SL(2, ℤ).
- Defined in
- Mathlib.NumberTheory.ModularForms.Cusps
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subgroup.IsArithmetic
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Matrix.SpecialLinearGroupstatement · cited by 348
- MonoidHom.rangestatement · cited by 314
- OnePointstatement and proof · cited by 126
- Matrix.SpecialLinearGroup.mapGLstatement · cited by 98
- IsCuspstatement · cited by 51
- Subgroup.IsArithmeticstatement and proof · cited by 41
- Subgroup.Commensurable.isCusp_iffproof · cited by 2
- Subgroup.IsArithmetic.is_commensurableproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- ModularForm.isZeroAt_of_coeffZero_eq_zeroproof · cited by 1
- ModularFormClass.bdd_at_infty_slashproof · cited by 1
- cosetToCuspOrbit_apply_mkstatement · cited by 0
- surjective_cosetToCuspOrbitproof · cited by 0
- CuspFormClass.zero_at_infty_slashproof · cited by 0