Translates of S-arithmetic orbits and applications
arXiv:2107.05017
Abstract
We prove that certain sequences of periodic orbits of the diagonal group in the space of lattices equidistribute. As an application we obtain new information regarding the sequence of best approximations to certain vectors with algebraic coordinates. In order to prove these results we generalize the seminal work of Eskin Mozes and Shah about the equidistribution of translates of periodic measures from the real case to the S-arithmetic case.
Minor changes on Theorem 1.2 and Theorem 1.4; add a proof of Theorem 1.5