Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

Lior Fishman; Keith Merrill; David Samuel Simmons

doi:10.1007/s00029-018-0446-7

Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

Lior Fishman, Keith Merrill, David Samuel Simmons

Mathematics

Research output: Contribution to journal › Article › peer-review

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).

Original language	English
Pages (from-to)	3875-3888
Number of pages	14
Journal	Selecta Mathematica, New Series
Volume	24
Issue number	5
Early online date	12 Oct 2018
DOIs	https://doi.org/10.1007/s00029-018-0446-7
Publication status	Published - Nov 2018

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10.1007/s00029-018-0446-7

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title = "Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces",

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{\textquoteright} 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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AB - 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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DO - 10.1007/s00029-018-0446-7

M3 - Article

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JO - Selecta Mathematica, New Series

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