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Diophantine transference inequalities : weighted, inhomogeneous, and intermediate exponents
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Chow, Sam, Ghosh, Anish, Marnat, Antoine and Simmons, David E. (2020) Diophantine transference inequalities : weighted, inhomogeneous, and intermediate exponents. Annali della Scuola Normale Superiore di Pisa , XXI . pp. 643-671. doi:10.2422/2036-2145.201808_013 ISSN 0391-173X.
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Official URL: https://doi.org/10.2422/2036-2145.201808_013
Abstract
We extend the Khintchine transference inequalities, as well as a
homogeneous-inhomogeneoustransference 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 BeresnevichVelani (2010) about inhomogeneous intermediate exponents.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Lattice theory, Diophantine approximation , Manifolds (Mathematics) | ||||||
Journal or Publication Title: | Annali della Scuola Normale Superiore di Pisa | ||||||
Publisher: | Classe di Scienze | ||||||
ISSN: | 0391-173X | ||||||
Official Date: | 22 December 2020 | ||||||
Dates: |
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Volume: | XXI | ||||||
Page Range: | pp. 643-671 | ||||||
DOI: | 10.2422/2036-2145.201808_013 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Copyright Holders: | © 2009-2016 Annali della Scuola Normale Superiore | ||||||
Date of first compliant deposit: | 18 September 2019 | ||||||
Date of first compliant Open Access: | 17 February 2021 | ||||||
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