Theorems · Definition · number theory
NumberField.InfinitePlace.nrComplexPlaces
(K : Type u_1) → [inst : Field K] → [NumberField K] → ℕ
The number of infinite complex places of the number field K.
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 141 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Fintype.cardproof · cited by 1,386
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlaceproof · cited by 604
- NumberField.InfinitePlace.IsComplexproof · cited by 272
Cited by56
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.convexBodyLTFactorproof · cited by 13
- NumberField.InfinitePlace.card_add_two_mul_card_eq_rankstatement and proof · cited by 9
- NumberField.mixedEmbedding.convexBodyLT'Factorproof · cited by 6
- IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_twostatement and proof · cited by 4
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisstatement and proof · cited by 4
- NumberField.dedekindZeta_residueproof · cited by 4
- NumberField.mixedEmbedding.convexBodySumFactorproof · cited by 4
- NumberField.mixedEmbedding.finrankproof · cited by 4
- NumberField.Ideal.tendsto_norm_le_div_atTop₀statement and proof · cited by 2
- NumberField.InfinitePlace.card_complex_embeddingsstatement and proof · cited by 2
- NumberField.InfinitePlace.card_eq_nrRealPlaces_add_nrComplexPlacesstatement and proof · cited by 2
- NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integralstatement and proof · cited by 2