Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

Badziahin, Dzmitry

doi:10.1016/j.aim.2009.08.005

Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

Badziahin, Dzmitry

Authors

Dzmitry Badziahin

Abstract

The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in RnRn 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.

Citation

Badziahin, D. (2010). Inhomogeneous Diophantine approximation on curves and Hausdorff dimension. Advances in Mathematics, 223(1), 329-351. https://doi.org/10.1016/j.aim.2009.08.005

Journal Article Type	Article
Publication Date	Jan 15, 2010
Deposit Date	May 30, 2011
Publicly Available Date	May 6, 2014
Journal	Advances in Mathematics
Print ISSN	0001-8708
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	223
Issue	1
Pages	329-351
DOI	https://doi.org/10.1016/j.aim.2009.08.005
Keywords	Diophantine approximation, Lebesgues measure, Hausdorff dimension, Non-degenerate curve, Khintchine theorem.

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Copyright Statement
This is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics, 223, 1, 2010, 10.1016/j.aim.2009.08.005.