Inhomogeneous theory of dual Diophantine approximation on manifolds

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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.
Original languageEnglish
Pages (from-to)1-35
Number of pages35
JournalAdvances in Mathematics
Issue number1
Early online date16 Oct 2012
Publication statusPublished - 15 Jan 2013

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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


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

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