Theorems · Theorem · number theory
ModularGroup.im_smul_eq_div_normSq
∀ (g : Matrix.SpecialLinearGroup (Fin 2) ℤ) (z : UpperHalfPlane),
(g • z).im =
z.im /
Complex.normSq
(UpperHalfPlane.denom (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) g))
↑z)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- MonoidHomstatement · cited by 3,629
- one_mulproof · cited by 2,841
- Units.valproof · cited by 1,966
- absproof · cited by 1,814
- MonoidWithZeroHomstatement · cited by 704
- UpperHalfPlanestatement and proof · cited by 626
- Matrix.GeneralLinearGroupstatement · cited by 556
- Matrix.SpecialLinearGroupstatement and proof · cited by 348
Cited by6
Results whose statement or proof uses this declaration.
- ModularGroup.cases_of_mem_fd_smul_mem_fdproof · cited by 2
- ModularGroup.exists_smul_mem_fdproof · cited by 2
- ModularGroup.exists_bound_of_invariant_of_isBigOproof · cited by 2
- ModularGroup.exists_max_improof · cited by 1
- ModularGroup.exists_one_half_le_im_smul_and_norm_denom_leproof · cited by 1
- ModularGroup.im_lt_im_S_smulproof · cited by 1