Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents

David Samuel Simmons; Sam Chow; Anish Ghosh; Lifan Guan; Antoine Marnat

doi:10.2422/2036-2145.201808_013

Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	643-671
Number of pages	29
Journal	Annali della Scuola Normale Superiore di Pisa. Classe di Scienze
Volume	21
Issue number	Special 2020
DOIs	https://doi.org/10.2422/2036-2145.201808_013
Publication status	Published - 22 Dec 2020

Bibliographical note

© 2020 Annali della Scuola Normale Superiore. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Access to Document

10.2422/2036-2145.201808_013

D.Simmons_AAM_1808.07184
© 2020 Annali della Scuola Normale Superiore. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
Accepted author manuscript, 325 KB

Cite this

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AU - Guan, Lifan

AU - Marnat, Antoine

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