Theorems · Theorem · number theory

NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : (NumberField.RingOfIntegers K)ˣ),
  ∑ w, (NumberField.Units.logEmbedding K) (Additive.ofMul x) w =
    -↑NumberField.Units.dirichletUnitTheorem.w₀.mult *
      Real.log (NumberField.Units.dirichletUnitTheorem.w₀ ((algebraMap (NumberField.RingOfIntegers K) K) ↑x))

Defined in: Mathlib.NumberTheory.NumberField.Units.DirichletTheorem
Cited by: 3 results in Mathlib
Foundations: Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites27

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

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Cited by3

Results whose statement or proof uses this declaration.

NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iffproof · cited by 2
NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_leproof · cited by 1
NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_topproof · cited by 0