Theorems · Theorem · number theory
ModularGroup.tendsto_normSq_coprime_pair
∀ (z : UpperHalfPlane), Filter.Tendsto (fun p => Complex.normSq (↑(p 0) * ↑z + ↑(p 1))) Filter.cofinite Filter.atTop
The function (c,d) → |cz+d|^2 is proper, that is, preimages of bounded-above sets are finite.
- Defined in
- Mathlib.NumberTheory.Modular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites70
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
- Moduleproof · cited by 20,661
- RingHom.idproof · cited by 18,349
- LinearMapproof · cited by 10,215
- Filterproof · cited by 8,121
- Complexstatement and proof · cited by 5,565
- Bot.botproof · cited by 4,720
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement and proof · cited by 3,814
- add_zeroproof · cited by 2,707
- Filter.atTopstatement and proof · cited by 2,405
Cited by1
Results whose statement or proof uses this declaration.
- ModularGroup.exists_max_improof · cited by 1