Theorems · Theorem · number theory
UpperHalfPlane.modular_S_smul
∀ (z : UpperHalfPlane), ModularGroup.S • z = { coe := (-↑z)⁻¹, coe_im_pos := ⋯ }- Cited by
- 9 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Algebra.algebraMapproof · cited by 4,706
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- UpperHalfPlanestatement and proof · cited by 626
Cited by9
Results whose statement or proof uses this declaration.
- SlashInvariantForm.slash_S_applyproof · cited by 1
- EisensteinSeries.tendsto_double_sum_S_actproof · cited by 1
- EisensteinSeries.G2_slash_actionproof · cited by 1
- ModularGroup.stabilizer_Iproof · cited by 0
- ModularGroup.stabilizer_of_neproof · cited by 0
- ModularGroup.stabilizer_ρproof · cited by 0
- UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zeroproof · cited by 0
- jacobiTheta_S_smulproof · cited by 0
- ModularForm.discriminant_S_invariantproof · cited by 0