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Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

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JournalAdvances in Mathematics
DatePublished - 15 Jan 2010
Issue number1
Volume223
Number of pages23
Pages (from-to)329-351
Original languageEnglish

Abstract

The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in R-n akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978) [2], Dodson, Dickinson (2000) [18] and Beresnevich, Bernik, Kleinbock, Margulis (2002) [8]. In the case of planar curves, the complete Hausdorff dimension theory is developed. (C) 2009 Elsevier Inc. All rights reserved.

    Research areas

  • Diophantine approximation, Lebesgues measure, Hausdorff dimension, Non-degenerate curve, Khintchine theorem, PLANAR CURVES, MANIFOLDS, THEOREM, CONVERGENCE

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