Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  MeasureTheory.volume (NumberField.mixedEmbedding.fundamentalCone.normLeOne K) =
    2 ^ NumberField.InfinitePlace.nrRealPlaces K * ↑NNReal.pi ^ NumberField.InfinitePlace.nrComplexPlaces K *
      ENNReal.ofReal (NumberField.Units.regulator K)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 2 results in Mathlib
Foundations: Depth 341 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites68

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

DFunLike.coestatement · cited by 62,936
Setstatement and proof · cited by 53,352
Realstatement and proof · cited by 25,697
Finsetproof · cited by 13,712
MeasureTheory.Measurestatement · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Fieldstatement and proof · cited by 7,404
Set.imageproof · cited by 5,609
Complexstatement · cited by 5,565
Finset.univproof · cited by 3,473
Finset.prodproof · cited by 2,356
Real.piproof · cited by 1,774

Cited by2

Results whose statement or proof uses this declaration.

NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTopproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOneproof · cited by 1