Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.realSpace K),
  NumberField.mixedEmbedding.logMap
        (NumberField.mixedEmbedding.mixedSpaceOfRealSpace (↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis x)) ∈
      ZSpan.fundamentalDomain
        (Module.Basis.ofZLatticeBasis ℝ (NumberField.Units.unitLattice K) (NumberField.Units.basisUnitLattice K)) ↔
    ∀ (w : NumberField.InfinitePlace K), w ≠ NumberField.Units.dirichletUnitTheorem.w₀ → x w ∈ Set.Ico 0 1

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 0 results in Mathlib
Foundations: Depth 337 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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