Theorems · Theorem · number theory
DirichletCharacter.card_eq_totient_of_hasEnoughRootsOfUnity
∀ (R : Type u_1) [inst : CommRing R] (n : ℕ) [NeZero n] [HasEnoughRootsOfUnity R (Monoid.exponent (ZMod n)ˣ)], Nat.card (DirichletCharacter R n) = n.totient
There are n.totient Dirichlet characters mod n with values in a ring that has enough
roots of unity.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Unitsstatement and proof · cited by 2,804
- ZModstatement and proof · cited by 1,024
- Nat.cardstatement and proof · cited by 844
- Nonempty.someproof · cited by 340
- Nat.card_eq_fintype_cardproof · cited by 200
- DirichletCharacterstatement and proof · cited by 161
- Nat.card_congrproof · cited by 133
- Monoid.exponentstatement and proof · cited by 128
- MulEquiv.toEquivproof · cited by 126
- Nat.totientstatement · cited by 111
- HasEnoughRootsOfUnitystatement and proof · cited by 56
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.sum_characters_eqproof · cited by 1