Theorems · Theorem · number theory
ModularForm.SL_slash_apply
∀ {k : ℤ} (f : UpperHalfPlane → ℂ) (γ : Matrix.SpecialLinearGroup (Fin 2) ℤ) (τ : UpperHalfPlane),
SlashAction.map k γ f τ =
f (γ • τ) *
UpperHalfPlane.denom (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ ^
(-k)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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 and proof · cited by 5,565
- Matrixstatement · cited by 4,303
- mul_oneproof · cited by 3,885
- MonoidHomstatement · cited by 3,629
- Units.valproof · cited by 1,966
- absproof · cited by 1,814
- Complex.ofRealproof · cited by 1,654
- UpperHalfPlanestatement and proof · cited by 626
- Matrix.GeneralLinearGroupstatement · cited by 556
- Matrix.SpecialLinearGroupstatement and proof · cited by 348
Cited by7
Results whose statement or proof uses this declaration.
- ModularForm.div_slash_SL2proof · cited by 1
- ModularForm.SL_smul_slashproof · cited by 1
- SlashInvariantForm.slash_S_applyproof · cited by 1
- EisensteinSeries.eisensteinSeries_slash_applyproof · cited by 1
- ModularForm.slash_action_eq'_iffproof · cited by 0
- ModularForm.discriminant_S_invariantproof · cited by 0
- ModularForm.discriminant_T_invariantproof · cited by 0