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Inhomogeneous theory of dual Diophantine approximation on manifolds

Badziahin, Dzmitry; Beresnevich, Victor; Velani, Sanju

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Authors

Dzmitry Badziahin

Victor Beresnevich

Sanju Velani



Abstract

The theory of inhomogeneous Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the Groshev type theory is established for all such manifolds. Our results naturally incorporate and generalize the homogeneous measure and dimension theorems for non-degenerate manifolds established to date. The results have natural applications beyond the standard inhomogeneous theory such as Diophantine approximation by algebraic integers.

Citation

Badziahin, D., Beresnevich, V., & Velani, S. (2013). Inhomogeneous theory of dual Diophantine approximation on manifolds. Advances in Mathematics, 232(1), 1-35. https://doi.org/10.1016/j.aim.2012.09.022

Journal Article Type Article
Acceptance Date Sep 5, 2012
Online Publication Date Oct 15, 2012
Publication Date Jan 15, 2013
Deposit Date May 30, 2011
Publicly Available Date Mar 28, 2024
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 232
Issue 1
Pages 1-35
DOI https://doi.org/10.1016/j.aim.2012.09.022
Keywords Metric Diophantine approximation, Extremal manifolds, Groshev type theorem, Ubiquitous systems.

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics, 232, 1, 2013, 10.1016/j.aim.2012.09.022.




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