Theorems · Theorem · number theory
jacobiSum_nontrivial_inv
∀ {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 χ χ⁻¹ = -χ (-1)If χ is a nontrivial multiplicative character on a finite field F,
then J(χ,χ⁻¹) = -χ(-1).
- Defined in
- Mathlib.NumberTheory.JacobiSum.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · 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
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- IsDomainstatement and proof · cited by 2,196
- map_mulproof · cited by 1,137
- sub_selfproof · cited by 996
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