Theorems · Theorem · number theory

NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero

∀ {K : Type u_1} [inst : Field K] {x : (NumberField.RingOfIntegers K)ˣ} {w : NumberField.InfinitePlace K},
  ↑w.mult * Real.log (w ((algebraMap (NumberField.RingOfIntegers K) K) ↑x)) = 0 ↔
    w ((algebraMap (NumberField.RingOfIntegers K) K) ↑x) = 1

Defined in: Mathlib.NumberTheory.NumberField.Units.DirichletTheorem
Cited by: 1 results in Mathlib
Foundations: Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapstatement and proof · cited by 4,706
Unitsstatement and proof · cited by 2,804
Nat.cast_oneproof · cited by 2,501
Units.valstatement and proof · cited by 1,966
Nat.cast_zeroproof · cited by 1,870
LT.lt.ne'proof · cited by 1,417
Real.logstatement · cited by 939
NumberField.InfinitePlacestatement and proof · cited by 604

Cited by1

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NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iffproof · cited by 2