Theorems · Theorem · number theory
gaussSum_pow_eq_prod_jacobiSum_aux
∀ {F : Type u_1} {R : Type u_2} [inst : Fintype F] [inst_1 : Field F] [inst_2 : CommRing R] [IsDomain R]
(χ : MulChar F R) (ψ : AddChar F R) {n : ℕ},
0 < n → n < orderOf χ → gaussSum χ ψ ^ n = gaussSum (χ ^ n) ψ * ∏ j ∈ Finset.Ico 1 n, jacobiSum χ (χ ^ j)- Defined in
- Mathlib.NumberTheory.JacobiSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- mul_oneproof · cited by 3,885
- Finset.prodstatement and proof · cited by 2,356
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- mul_assocproof · cited by 1,667
- pow_oneproof · cited by 894
- Finset.prod_congrproof · cited by 646
- Finset.Icostatement and proof · cited by 450
- pow_succproof · cited by 374
Cited by1
Results whose statement or proof uses this declaration.
- gaussSum_pow_eq_prod_jacobiSumproof · cited by 0