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Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

Research group:
Pure Mathematics | Number Theory
TitleInhomogeneous Diophantine approximation on curves and Hausdorff dimension
Publication TypeJournal Article
Year of Publication2010
AuthorsBadziahin D
Refereed DesignationRefereed
JournalAdvances in Mathematics
Volume223
Start Page329
Issue1
Pagination329 -- 351
Date Published01/2010
AbstractThe 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.

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Edited 28 Sep 2010 - 20:12 by vb8

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