Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one
∀ (p k : ℕ) [hp : Fact (Nat.Prime p)] {K : Type u_1} [inst : Field K] [inst_1 : NumberField K]
[hK : IsCyclotomicExtension {p ^ (k + 1)} ℚ K] {ζ : K} (hζ : IsPrimitiveRoot ζ (p ^ (k + 1))),
Associated ((Algebra.norm ℤ) (hζ.toInteger - 1)) ↑p- Cited by
- 3 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- MonoidHomstatement · cited by 3,629
- Factstatement and proof · cited by 2,726
- zero_addproof · cited by 2,366
- Nat.Primestatement and proof · cited by 2,059
- pow_oneproof · cited by 894
- add_assocproof · cited by 746
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement · cited by 413
- IsPrimitiveRootstatement and proof · cited by 356
Cited by3
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_oneproof · cited by 2
- IsCyclotomicExtension.Rat.zeta_sub_one_dvd_intCast_iffproof · cited by 1
- IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_powproof · cited by 1