Theorems · Theorem · number theory

IsPrimitiveRoot.integralPowerBasisOfPrimePow_dim

∀ {p k : ℕ} {K : Type u} [inst : Field K] {ζ : K} [hp : Fact (Nat.Prime p)] [inst_1 : CharZero K]
  [hcycl : IsCyclotomicExtension {p ^ k} ℚ K] (hζ : IsPrimitiveRoot ζ (p ^ k)),
  hζ.integralPowerBasisOfPrimePow.dim = (p ^ k).totient

Defined in: Mathlib.NumberTheory.NumberField.Cyclotomic.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Fact CharZero IsCyclotomicExtension

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Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Fieldstatement and proof · cited by 7,404
Factstatement and proof · cited by 2,726
Nat.Primestatement and proof · cited by 2,059
Polynomial.natDegreeproof · cited by 1,105
CharZerostatement and proof · cited by 932
NumberField.RingOfIntegersstatement · cited by 413
IsPrimitiveRootstatement and proof · cited by 356
IsCyclotomicExtensionstatement and proof · cited by 220
Nat.totientstatement and proof · cited by 111
PowerBasis.dimstatement · cited by 74
NeZero.posproof · cited by 57

Cited by1

Results whose statement or proof uses this declaration.

IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_twoproof · cited by 1