Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.realSpace K),
  ∏ w,
      NumberField.mixedEmbedding.fundamentalCone.deriv_expMap_single w
        ((NumberField.mixedEmbedding.fundamentalCone.completeBasis K).equivFun.symm x w) =
    Real.exp (x NumberField.Units.dirichletUnitTheorem.w₀) ^ Module.finrank ℚ K *
        (∏ w, ↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis x ↑w)⁻¹ *
      2⁻¹ ^ NumberField.InfinitePlace.nrComplexPlaces K

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by: 1 results in Mathlib
Foundations: Depth 336 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites45

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
RingHom.idstatement · cited by 18,349
Finsetproof · cited by 13,712
Fieldstatement and proof · cited by 7,404
mul_oneproof · cited by 3,885
Finset.univstatement and proof · cited by 3,473
LinearEquivstatement · cited by 3,317
one_mulproof · cited by 2,841
Nat.cast_oneproof · cited by 2,501
Finset.prodstatement and proof · cited by 2,356
Module.finrankstatement and proof · cited by 1,770

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasisproof · cited by 1