Equidistribution of values of linear forms on quadratic surfaces

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 a previous paper. The methods used are based on those developed by A. Eskin, S. Mozes and G. Margulis. Specifically, they rely on equidistribution properties of unipotent flows.