Theorems · Theorem · number theory
gaussSum_sq
∀ {R : Type u} [inst : Field R] [inst_1 : Fintype R] {R' : Type v} [inst_2 : CommRing R'] [IsDomain R']
{χ : MulChar R R'},
χ ≠ 1 → χ.IsQuadratic → ∀ {ψ : AddChar R R'}, ψ.IsPrimitive → gaussSum χ ψ ^ 2 = χ (-1) * ↑(Fintype.card R)When χ is a nontrivial quadratic character, then the square of gaussSum χ ψ
is χ(-1) times the cardinality of R.
- Defined in
- Mathlib.NumberTheory.GaussSum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 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
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- Fintype.cardstatement and proof · cited by 1,386
- AddCharstatement and proof · cited by 286
- MulCharstatement and proof · cited by 186
- pow_twoproof · cited by 150
- gaussSumstatement and proof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- Char.card_pow_cardproof · cited by 1