Linnik's ergodic method and the distribution of integer points on spheres
Number Theory
2010-01-07 v1 Dynamical Systems
Abstract
We discuss Linnik's work on the distribution of integral solutions to , as 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, -functions).
Keywords
Cite
@article{arxiv.1001.0897,
title = {Linnik's ergodic method and the distribution of integer points on spheres},
author = {Jordan S. Ellenberg and Philippe Michel and Akshay Venkatesh},
journal= {arXiv preprint arXiv:1001.0897},
year = {2010}
}