Theorems · Theorem · number theory

NumberField.mixedEmbedding.logMap_apply

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.mixedSpace K)
  (w : { w // w ≠ NumberField.Units.dirichletUnitTheorem.w₀ }),
  NumberField.mixedEmbedding.logMap x w =
    ↑(↑w).mult *
      (Real.log ((NumberField.mixedEmbedding.normAtPlace ↑w) x) -
        Real.log (NumberField.mixedEmbedding.norm x) * (↑(Module.finrank ℚ K))⁻¹)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
Cited by: 2 results in Mathlib
Foundations: Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites17

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

DFunLike.coestatement · cited by 62,936
Realstatement · cited by 25,697
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Module.finrankstatement · cited by 1,770
Real.logstatement · cited by 939
MonoidWithZeroHomstatement · cited by 704
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.IsRealstatement · cited by 301
NumberField.InfinitePlace.IsComplexstatement · cited by 272
NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.logMap_realproof · cited by 1
NumberField.mixedEmbedding.logMap_apply_of_norm_eq_oneproof · cited by 0