Theorems · Theorem · number theory

NumberField.dedekindZeta_residue_def

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  NumberField.dedekindZeta_residue K =
    2 ^ NumberField.InfinitePlace.nrRealPlaces K * (2 * Real.pi) ^ NumberField.InfinitePlace.nrComplexPlaces K *
          NumberField.Units.regulator K *
        ↑(NumberField.classNumber K) /
      (↑(NumberField.Units.torsionOrder K) * √|↑(NumberField.discr K)|)

Defined in: Mathlib.NumberTheory.NumberField.DedekindZeta
Cited by: 0 results in Mathlib
Foundations: Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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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
absstatement · cited by 1,814
Real.pistatement · cited by 1,774
NumberFieldstatement and proof · cited by 653
Real.sqrtstatement · cited by 545
NumberField.discrstatement · cited by 53
NumberField.InfinitePlace.nrComplexPlacesstatement · cited by 52
NumberField.InfinitePlace.nrRealPlacesstatement · cited by 33
NumberField.Units.regulatorstatement · cited by 19
NumberField.Units.torsionOrderstatement · cited by 17
NumberField.classNumberstatement · cited by 7

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