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Selecta Mathematica

, Volume 24, Issue 5, pp 3875–3888 | Cite as

Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

  • Lior Fishman
  • Keith Merrill
  • David Simmons
Article
  • 26 Downloads

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).

Mathematics Subject Classification

11J13 11J83 

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Notes

Acknowledgements

The first-named author was supported in part by the Simons Foundation Grant #245708.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North TexasDentonUSA
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA
  3. 3.Department of MathematicsOhio State UniversityColumbusUSA

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