Theorems · Theorem · number theory

AddChar.sum_mulShift

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : Fintype R] [inst_2 : DecidableEq R] {R' : Type u_2}
  [inst_3 : CommRing R'] [IsDomain R'] {ψ : AddChar R R'} (b : R),
  ψ.IsPrimitive → ∑ x, ψ (x * b) = ↑(if b = 0 then Fintype.card R else 0)

The sum over the values of mulShift ψ b for ψ primitive is zero when b ≠ 0 and #R otherwise.

Defined in

Mathlib.NumberTheory.LegendreSymbol.AddCharacter

Cited by

2 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFintypeDecidableEqCommRingIsDomain