Theorems · Theorem · number theory
jacobiSum_one_nontrivial
∀ {F : Type u_1} {R : Type u_2} [inst : Field F] [inst_1 : Fintype F] [inst_2 : CommRing R] [IsDomain R]
{χ : MulChar F R}, χ ≠ 1 → jacobiSum 1 χ = -1If χ is a nontrivial multiplicative character on a finite field F, then J(1,χ) = -1.
- Defined in
- Mathlib.NumberTheory.JacobiSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Unitsproof · cited by 2,804
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- IsDomainstatement and proof · cited by 2,196
- MulZeroClass.zero_mulproof · cited by 1,625
- IsUnitproof · cited by 1,602
Cited by1
Results whose statement or proof uses this declaration.
- exists_jacobiSum_eq_neg_one_addproof · cited by 0