Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {x : K},
  x ≠ 0 →
    ∑ w,
        ↑NumberField.mixedEmbedding.fundamentalCone.expMap.symm
          (NumberField.mixedEmbedding.normAtAllPlaces ((NumberField.mixedEmbedding K) x)) w =
      Real.log ↑|(Algebra.norm ℚ) x|

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 2 results in Mathlib
Foundations: Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites32

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
Finsetproof · cited by 13,712
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Finset.sumstatement and proof · cited by 5,195
MonoidHomstatement · cited by 3,629
Finset.univstatement and proof · cited by 3,473
FunLikeproof · cited by 2,560
Finset.sum_congrproof · cited by 2,323
absstatement · cited by 1,814

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamilyproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symmproof · cited by 1