MathAudit

Publication metadata

Journal citation
Moscow Mathematical Journal 5(4), 747–766 (2005)
Publication date
2005
arXiv counterpart
arXiv:math/0406065 ↗
MSC 2020
11J20, 11J13, 11J82
As specified in the publication (MSC 2000)
11J20, 11J13, 11J82 ↗Publication metadataAll three codes carry forward unchanged through the official conversion tables.

Abstract

The paper develops homogeneous-to-inhomogeneous transference through Diophantine exponents. Its best-approximation growth and transference lemmas are used in the fixed-matrix dependence graph.

Role in dependence graphs

Proof-critical source

Metric theory with a fixed matrix

This paper is included only for the following marked statements:

  • Lemma 1 · §2, immediately after equations (4)–(5)A sequence of best-approximation denominators grows at least geometrically. Bugeaud–Laurent give the full pigeonhole proof.
  • Lemma 3 · §3, Transference lemmaTurns a uniform lower bound for the transpose into an inhomogeneous approximation for every shift. Its reproduced proof invokes Cassels, Chapter V, Theorem XVII, Part B.

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