Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents

Sam Chow, Anish Ghosh, Lifan Guan, Antoine Marnat, David Simmons

Research output: Contribution to journalArticleResearch

Abstract

We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine approximation on manifolds and to weighted badly approximable vectors. Finally, we interpret and prove a conjecture of Beresnevich-Velani (2010) about inhomogeneous intermediate exponents.
Original languageUndefined/Unknown
JournalarXiv.org e-Print archive
Publication statusPublished - 22 Aug 2018

Keywords

  • math.NT
  • 11J83

Cite this

Diophantine transference inequalities : weighted, inhomogeneous, and intermediate exponents. / Chow, Sam; Ghosh, Anish; Guan, Lifan; Marnat, Antoine; Simmons, David.

In: arXiv.org e-Print archive, 22.08.2018.

Research output: Contribution to journalArticleResearch

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AB - We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine approximation on manifolds and to weighted badly approximable vectors. Finally, we interpret and prove a conjecture of Beresnevich-Velani (2010) about inhomogeneous intermediate exponents.

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