Theorems · Theorem · number theory

IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow

∀ {n : ℕ} [inst : NeZero n] {K : Type u} (L : Type v) [inst_1 : Field K] [inst_2 : Field L] [inst_3 : Algebra K L],
  IsPrimePow n →
    ∀ [inst_4 : IsCyclotomicExtension {n} K L],
      Irreducible (Polynomial.cyclotomic n K) →
        n ≠ 2 → (Algebra.norm K) (IsCyclotomicExtension.zeta n K L - 1) = ↑n.minFac

If IsPrimePow n, n ≠ 2 and Irreducible (cyclotomic n K) (in particular for K = ℚ), then the norm of zeta n K L - 1 is n.minFac.

Defined in

Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots

Cited by

0 results in Mathlib

Foundations

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

Assumes

NeZeroFieldFieldAlgebraIsCyclotomicExtension