Theorems · Theorem · number theory

NumberField.exists_ideal_in_class_of_norm_le

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (C : ClassGroup (NumberField.RingOfIntegers K)),
  ∃ I,
    ClassGroup.mk0 I = C ∧
      ↑(Ideal.absNorm ↑I) ≤
        (4 / Real.pi) ^ NumberField.InfinitePlace.nrComplexPlaces K *
          (↑(Module.finrank ℚ K).factorial / ↑(Module.finrank ℚ K) ^ Module.finrank ℚ K * √|↑(NumberField.discr K)|)

Defined in: Mathlib.NumberTheory.NumberField.ClassNumber
Cited by: 1 results in Mathlib
Foundations: Depth 313 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites60

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
SetLike.coeproof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Idealstatement and proof · cited by 4,748
Algebra.algebraMapproof · cited by 4,706
MonoidHomstatement · cited by 3,629
Submonoidstatement · cited by 3,086
mul_commproof · cited by 2,262
MulZeroClass.mul_zeroproof · cited by 2,091
Units.valproof · cited by 1,966
absstatement and proof · cited by 1,814

Cited by1

Results whose statement or proof uses this declaration.

RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_norm_leproof · cited by 2