Theorems · Theorem · number theory
jacobiSum_eq_sum_sdiff
∀ {F : Type u_1} {R : Type u_2} [inst : CommRing F] [Nontrivial F] [inst_2 : Fintype F] [inst_3 : DecidableEq F]
[inst_4 : CommRing R] (χ ψ : MulChar F R), jacobiSum χ ψ = ∑ x ∈ Finset.univ \ {0, 1}, χ x * ψ (1 - x)The Jacobi sum of two multiplicative characters on a nontrivial finite commutative ring F
can be written as a sum over F \ {0,1}.
- Defined in
- Mathlib.NumberTheory.JacobiSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.univstatement and proof · cited by 3,473
- add_zeroproof · cited by 2,707
- Nontrivialstatement and proof · cited by 2,416
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- sub_eq_add_negproof · cited by 1,023
Cited by1
Results whose statement or proof uses this declaration.
- jacobiSum_trivial_trivialproof · cited by 1