Theorems · Theorem · number theory

gaussSum_mulShift_of_isPrimitive

∀ {N : ℕ} [inst : NeZero N] {R : Type u_1} [inst_1 : CommRing R] (e : AddChar (ZMod N) R) [IsDomain R]
  {χ : DirichletCharacter R N}, χ.IsPrimitive → ∀ (a : ZMod N), gaussSum χ (e.mulShift a) = χ⁻¹ a * gaussSum χ e

If χ is a primitive character, then the function a ↦ gaussSum χ (e.mulShift a), for any fixed additive character e, is a constant multiple of χ⁻¹.

Defined in

Mathlib.NumberTheory.DirichletCharacter.GaussSum

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NeZeroCommRingIsDomain