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Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

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JournalSelecta Mathematica, New Series
DateE-pub ahead of print - 12 Oct 2018
DatePublished (current) - Nov 2018
Issue number5
Volume24
Number of pages14
Pages (from-to)3875-3888
Early online date12/10/18
Original languageEnglish

Abstract

We prove an analogue of a theorem of Pollington and Velani (Sel Math (N.S.) 11:297–307, 2005), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof incorporates the framework of intrinsic approximation on such hypersurfaces first developed in the authors’ joint work with Kleinbock (Intrinsic Diophantine approximation on manifolds, 2014. arXiv:1405.7650v2) with ideas from work of Kleinbock et al. (Sel Math (N.S.) 10:479–523, 2004).

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