%0 Journal Article
%T Linnik's ergodic method and the distribution of integer points on spheres
%A Jordan S. Ellenberg
%A Philippe Michel
%A Akshay Venkatesh
%J Mathematics
%D 2010
%I arXiv
%X We discuss Linnik's work on the distribution of integral solutions to $x^2+y^2+z^2 =d$, as $d$ goes to infinity. We give an exposition of Linnik's ergodic method; indeed, by using large-deviation results for random walks on expander graphs, we establish a refinement of his equidistribution theorem. We discuss the connection of these ideas with modern developments (ergodic theory on homogeneous spaces, $L$-functions).
%U http://arxiv.org/abs/1001.0897v1