Theorems · Theorem · number theory

NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] {f : NumberField.InfinitePlace K → NNReal},
  NumberField.mixedEmbedding.minkowskiBound K 1 < MeasureTheory.volume (NumberField.mixedEmbedding.convexBodyLT K f) →
    ∃ a, a ≠ 0 ∧ ∀ (w : NumberField.InfinitePlace K), w ↑a < ↑(f w)

A version of exists_ne_zero_mem_ideal_lt for the ring of integers of K.

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody
Cited by: 2 results in Mathlib
Foundations: Depth 312 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cited by2

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NumberField.Units.dirichletUnitTheorem.seq_nextproof · cited by 3
NumberField.mixedEmbedding.exists_primitive_element_lt_of_isRealproof · cited by 1