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

## TL;DR

This paper extends a method to establish precise effective equidistribution results for translates of horospheres in homogeneous spaces formed by semisimple Lie groups and lattices, advancing understanding of their dynamical behavior.

## Contribution

It generalizes Burger's method to obtain effective equidistribution results for horosphere translates in $\Gammaackslash G$, a significant step in homogeneous dynamics.

## Key findings

- Effective equidistribution results for horosphere translates
- Generalization of Burger's method to new settings
- Enhanced understanding of dynamical properties in homogeneous spaces

## 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 $\Gamma\backslash G$.