Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

Details Inhomogeneous Diophantine approximation on curves and Hausdorff dimension Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

2008-09-23

arxiv.org/abs/0809.3937v1

Mathematics

Number Theory

28 pages

Scientific paper

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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