On the rate of equidistribution of expanding translates of horospheres in $\Gamma \backslash G$

Abstract

Let $G$ be a semisimple Lie group and $\Gamma$ a lattice in $G$. We generalize a method of Burger to prove precise effective equidistribution results for translates of pieces of horospheres in the homogeneous space $\Gamma \backslash G$.