  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.
