Theorems · Theorem · number theory
SlashInvariantForm.slash_S_apply
∀ (f : UpperHalfPlane → ℂ) (k : ℤ) (z : UpperHalfPlane),
SlashAction.map k ModularGroup.S f z = f { coe := (-↑z)⁻¹, coe_im_pos := ⋯ } * ↑z ^ (-k)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Complex.ofRealproof · cited by 1,654
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- UpperHalfPlanestatement and proof · cited by 626
- Int.cast_oneproof · cited by 371
- Matrix.SpecialLinearGroupstatement · cited by 348
- Matrix.ofproof · cited by 336
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.G2_slash_actionproof · cited by 1