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Inhomogeneous Diophantine approximation on planar curves

Research group:
Number Theory
TitleInhomogeneous Diophantine approximation on planar curves
Publication TypeJournal Article
Year of Publication2011
AuthorsBeresnevich V, Vaughan R, Velani S
Refereed DesignationRefereed
Journal Math. Annalen
Volume349, no. 4
Pagination929-942
AbstractThe inhomogeneous metric theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann. of Math. (2), 166 (2007), pp. 367-426] and [Invent. Math., 166 (2006), pp. 103-124]. The key lies in obtaining essentially the best possible results regarding the distribution of `shifted' rational points near planar curves.
URLhttp://arxiv.org/abs/0903.2817
DOIDOI: 10.1007/s00208-010-0548-9
E-print numberarXiv:0903.2817

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Edited 18 Oct 2011 - 15:10 by slv3

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