Equidistribution of values of linear forms on quadratic surfaces
Number Theory
2016-01-20 v3 Dynamical Systems
Abstract
In this paper we investigate the distribution of the set of values of a linear map at integer points on a quadratic surface. In particular, it is shown that subject to certain algebraic conditions, this set is equidistributed. This can be thought of as a quantitative version of the main result from [2011arXiv1111.4428S]. The methods used are based on those developed by A. Eskin, S. Mozes and G. Margulis in [MR1609447]. Specifically, they rely on equidistribution properties of unipotent flows.
Cite
@article{arxiv.1303.0234,
title = {Equidistribution of values of linear forms on quadratic surfaces},
author = {Oliver Sargent},
journal= {arXiv preprint arXiv:1303.0234},
year = {2016}
}
Comments
27 pages. Section 3 has been rewritten