Theorems · Theorem · number theory
MulChar.IsQuadratic.pow_char
∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommRing R'] {χ : MulChar R R'},
χ.IsQuadratic → ∀ (p : ℕ) [hp : Fact (Nat.Prime p)] [CharP R' p], χ ^ p = χThe pth power of a quadratic character is itself, when p is the (prime) characteristic
of the target ring.
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommRingFactCharP
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Unitsproof · cited by 2,804
- Factstatement and proof · cited by 2,726
- CommMonoidstatement and proof · cited by 2,264
- Nat.Primestatement and proof · cited by 2,059
- Units.valproof · cited by 1,966
- one_powproof · cited by 521
- CharPstatement and proof · cited by 478
- zero_powproof · cited by 361
- Fact.outproof · cited by 328
- MulCharstatement and proof · cited by 186
Cited by2
Results whose statement or proof uses this declaration.
- MulChar.IsQuadratic.gaussSum_frobproof · cited by 1
- MulChar.IsQuadratic.gaussSum_frob_iterproof · cited by 1