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arXiv · 0809.3937

Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

Dzmitry Badziahin
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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), Dodson, Dickinson (2000) and Beresnevich, Bernik, Kleinbock, Margulis (2002). In the case of planar curves, the complete Hausdorff dimension theory is developed

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Dzmitry Badziahin. 2008-09-23. Inhomogeneous Diophantine approximation on curves and Hausdorff dimension. https://arxiv.org/abs/0809.3937

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