Theorems · Theorem · number theory

IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one

∀ {n : ℕ} [inst : NeZero n] {K : Type u} [inst_1 : Field K] [inst_2 : CharZero K] {ζ : K}
  [ce : IsCyclotomicExtension {n} ℚ K] (hζ : IsPrimitiveRoot ζ n),
  Algebra.discr ℚ ⇑(IsPrimitiveRoot.powerBasis ℚ hζ).basis =
    Algebra.discr ℚ ⇑(IsPrimitiveRoot.subOnePowerBasis ℚ hζ).basis

The discriminant of the power basis given by a primitive root of unity ζ is the same as the discriminant of the power basis given by ζ - 1.

Defined in

Mathlib.NumberTheory.Cyclotomic.Discriminant

Cited by

4 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NeZeroFieldCharZeroIsCyclotomicExtension