Theorems · Theorem · number theory
NumberField.InfinitePlace.IsPrimitiveRoot.nrRealPlaces_eq_zero_of_two_lt
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {ζ : K} {k : ℕ},
2 < k → IsPrimitiveRoot ζ k → NumberField.InfinitePlace.nrRealPlaces K = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexproof · cited by 5,565
- Norm.normproof · cited by 5,413
- absproof · cited by 1,814
- Complex.reproof · cited by 882
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlaceproof · cited by 604
- Complex.improof · cited by 591
- DFunLikeproof · cited by 576
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.nrRealPlaces_eq_zeroproof · cited by 3
- NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrankproof · cited by 1