Inhomogeneous theory of dual Diophantine approximation on manifolds

Badziahin, Dzmitry; Beresnevich, Victor; Velani, Sanju

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: May 7, 2014
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1508106