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Khinchin theorem for integral points on quadratic varieties

Number Theory 2018-12-07 v1 Representation Theory

Abstract

We prove an analogue the Khinchin theorem for the Diophantine approximation by integer vectors lying on a quadratic variety. The proof is based on the study of a dynamical system on a homogeneous space of the orthogonal group. We show that in this system, generic trajectories visit a family of shrinking subsets infinitely often.

Keywords

Cite

@article{arxiv.0804.3530,
  title  = {Khinchin theorem for integral points on quadratic varieties},
  author = {Alexander Gorodnik and Nimish A. Shah},
  journal= {arXiv preprint arXiv:0804.3530},
  year   = {2018}
}

Comments

19 pages

R2 v1 2026-06-21T10:33:32.335Z