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Abstract: 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-sergodic method; indeed, by using large-deviation results for random walks onexpander graphs, we establish a refinement of his equidistribution theorem. Wediscuss the connection of these ideas with modern developments ergodic theoryon homogeneous spaces, $L$-functions.



Author: Jordan S. Ellenberg, Philippe Michel, Akshay Venkatesh

Source: https://arxiv.org/



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