Theorems · Theorem · number theory
isCusp_SL2Z_iff
∀ {c : OnePoint ℝ}, IsCusp c (Matrix.SpecialLinearGroup.mapGL ℝ).range ↔ c ∈ Set.range (OnePoint.map Rat.cast)The cusps of SL(2, ℤ) are precisely the elements of ℙ¹(ℚ).
- Defined in
- Mathlib.NumberTheory.ModularForms.Cusps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites59
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHomproof · cited by 10,189
- Algebra.algebraMapproof · cited by 4,706
- Set.rangestatement and proof · cited by 4,705
- Matrixstatement · cited by 4,303
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Units.valproof · cited by 1,966
- Nat.cast_zeroproof · cited by 1,870
Cited by3
Results whose statement or proof uses this declaration.
- isCusp_SL2Z_iff'proof · cited by 7
- cosetToCuspOrbit_apply_mkstatement · cited by 0
- surjective_cosetToCuspOrbitproof · cited by 0