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Inhomogeneous theory of dual Diophantine approximation on manifolds

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JournalAdvances in Mathematics
DateE-pub ahead of print - 16 Oct 2012
DatePublished (current) - 15 Jan 2013
Issue number1
Volume232
Number of pages35
Pages (from-to)1-35
Early online date16/10/12
Original languageEnglish

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.

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©2012 Elsevier Inc. 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

    Research areas

  • Diophantine approximation, extremal manifolds, ubiquitous systems, Groshev type theorem

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