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.
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