Inhomogeneous Diophantine approximation on planar curves

V. V. Beresnevich, Robert Charles Vaughan, S. L. Velani

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper we develop the inhomogeneous metric theory of simultaneous Diophantine approximation on planar curves. Our results naturally extend the homogeneous Khintchine and Jarník type theorems established in Beresnevich et al. (Ann Math 166(2):367-426, 2007) and Vaughan and Velani (Invent Math 166:103-124, 2006) and are the first of their kind. The key lies in obtaining essentially the best possible results regarding the distribution of 'shifted' rational points near planar curves.

Original languageEnglish (US)
Pages (from-to)929-942
Number of pages14
JournalMathematische Annalen
Volume349
Issue number4
DOIs
StatePublished - Apr 1 2011

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Planar Curves
Diophantine Approximation
Simultaneous Approximation
Rational Points
Metric
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Beresnevich, V. V. ; Vaughan, Robert Charles ; Velani, S. L. / Inhomogeneous Diophantine approximation on planar curves. In: Mathematische Annalen. 2011 ; Vol. 349, No. 4. pp. 929-942.
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Inhomogeneous Diophantine approximation on planar curves. / Beresnevich, V. V.; Vaughan, Robert Charles; Velani, S. L.

In: Mathematische Annalen, Vol. 349, No. 4, 01.04.2011, p. 929-942.

Research output: Contribution to journalArticle

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