Theorems · Theorem · number theory

IsCyclotomicExtension.norm_zeta_pow_sub_one_two

∀ {K : Type u} (L : Type v) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {k : ℕ},
  2 ≤ k →
    ∀ [inst_3 : IsCyclotomicExtension {2 ^ k} K L],
      Irreducible (Polynomial.cyclotomic (2 ^ k) K) → (Algebra.norm K) (IsCyclotomicExtension.zeta (2 ^ k) K L - 1) = 2

If Irreducible (cyclotomic (2 ^ k) K) (in particular for K = ℚ) and k is at least 2, then the norm of zeta (2 ^ k) K L - 1 is 2.

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

FieldFieldAlgebraIsCyclotomicExtension