Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces
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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).
Mathematics Subject Classification11J13 11J83
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The first-named author was supported in part by the Simons Foundation Grant #245708.
- 5.Fishman, L., Kleinbock, D., Merrill, K., Simmons, D.: Intrinsic Diophantine approximation on manifolds, arXiv:1405.7650v2, preprint (2014)
- 8.Kleinbock, D., de Saxcé, N.: Rational approximation on quadrics: a simplex lemma and its consequences, arXiv:1808.07070, preprint (2018)