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Theorems · Definition · number theory

NumberField.Units.logEmbedding

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      Additive (NumberField.RingOfIntegers K)ˣ →+ NumberField.Units.dirichletUnitTheorem.logSpace K

The logarithmic embedding of the units (seen as an Additive group).

Defined in
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem
Cited by
25 results in Mathlib
Foundations
Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.Units.unitLattice · cited by 21Units.unitLatticeNumberField.Units.IsMaxRank · cited by 12Units.IsMaxRankNumberField.Units.isMaxRank_fundSystem · cited by 4Units.isMaxRank_fundSystemNumberField.Units.logEmbedding_fundSystem · cited by 4Units.logEmbedding_fundSy…NumberField.Units.regOfFamily_eq_det' · cited by 3Units.regOfFamily_eq_det'NumberField.Units.basisOfIsMaxRank_apply · cited by 3Units.basisOfIsMaxRank_ap…NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component · cited by 3dirichletUnitTheorem.sum_…NumberField.Units.logEmbeddingQuot · cited by 2Units.logEmbeddingQuotNumberField.mixedEmbedding.logMap_eq_logEmbedding · cited by 2mixedEmbedding.logMap_eq_…NumberField.mixedEmbedding.logMap_unit_smul · cited by 2mixedEmbedding.logMap_uni…NumberField.Units.dirichletUnitTheorem.logEmbedding_component · cited by 2dirichletUnitTheorem.logE…NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff · cited by 2dirichletUnitTheorem.logE…NumberField.Units.dirichletUnitTheorem.logEmbedding_ker · cited by 2dirichletUnitTheorem.logE…NumberField.Units.isMaxRank_iff_closure_finiteIndex · cited by 1Units.isMaxRank_iff_closu…NumberField.Units.logEmbeddingEquiv_apply · cited by 1Units.logEmbeddingEquiv_a…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapAddMonoidHom · cited by 3230AddMonoidHomUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valReal.log · cited by 939Real.logNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersAdditive · cited by 356AdditiveAdditive.toMul · cited by 109Additive.toMulNumberField.InfinitePlace.mult · cited by 107InfinitePlace.multNumberField.Units.dirichletUnitTheorem.w₀ · cited by 72dirichletUnitTheorem.w₀Units.logEmbeddingCITED BYCITES

Cites16

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

Cited by28

Results whose statement or proof uses this declaration.