Theorems · Theorem · number theory
ModularGroup.coe_fd
UpperHalfPlane.coe '' ModularGroup.fd = {z | 0 < z.im ∧ 1 ≤ ‖z‖ ∧ |z.re| ≤ 1 / 2}Explicit formula for the image of ModularGroup.fd in ℂ.
- Defined in
- Mathlib.NumberTheory.Modular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.ofPredstatement and proof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Set.extproof · cited by 2,266
- absstatement and proof · cited by 1,814
- Complex.restatement and proof · cited by 882
- UpperHalfPlanestatement and proof · cited by 626
- Complex.imstatement and proof · cited by 591
- UpperHalfPlane.coestatement and proof · cited by 288
Cited by1
Results whose statement or proof uses this declaration.
- ModularGroup.isClosed_coe_fdproof · cited by 0