Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.expMap_apply

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.realSpace K)
  (w : NumberField.InfinitePlace K),
  ↑NumberField.mixedEmbedding.fundamentalCone.expMap x w = Real.exp ((↑w.mult)⁻¹ * x w)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 1 results in Mathlib
Foundations: Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites9

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

Realstatement · cited by 25,697
Fieldstatement and proof · cited by 7,404
Real.expstatement · cited by 871
OpenPartialHomeomorph.toFun'statement · cited by 745
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.multstatement · cited by 107
NumberField.mixedEmbedding.realSpacestatement and proof · cited by 87
NumberField.mixedEmbedding.fundamentalCone.expMapstatement · cited by 23

Cited by1

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NumberField.mixedEmbedding.fundamentalCone.logMap_expMapproof · cited by 1