Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] {n : ℕ},
  0 < n →
    ∫⁻ (x : NumberField.mixedEmbedding.realSpace K) in NumberField.mixedEmbedding.fundamentalCone.paramSet K,
        ENNReal.ofReal (Real.exp (x NumberField.Units.dirichletUnitTheorem.w₀ * ↑n)) =
      (↑n)⁻¹

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 1 results in Mathlib
Foundations: Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites59

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Realstatement and proof · cited by 25,697
Finsetproof · cited by 13,712
MeasureTheory.Measureproof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Fieldstatement and proof · cited by 7,404
Set.univproof · cited by 3,945
mul_oneproof · cited by 3,885
Finset.univproof · cited by 3,473
mul_commproof · cited by 2,262
MulZeroClass.mul_zeroproof · cited by 2,091

Cited by1

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NumberField.mixedEmbedding.fundamentalCone.volume_normLeOneproof · cited by 2