Count lifts of non-maximal closed horocycles on $S{L}_N(\mathbb{Z})\backslash S{L}_N(\mathbb{R})/S{O}_N(\mathbb{R})$

Abstract

A closed horocycle $\mathcal{U}$ on $S{L}_N(\mathbb{Z})\backslash S{L}_N(\mathbb{R})/S{O}_N(\mathbb{R})$ has many lifts to the universal cover $S{L}_N(\mathbb{R})/S{O}_N(\mathbb{R})$. Under some conditions on the horocycle, we give a precise asymptotic count of its lifts of bounded distance away from a given base point in the universal cover. This partially generalizes previous work of Mohammadi--Golsefidy.

Some typos corrected. 25 pages