# On the remainder term of the Weyl law for congruence subgroups of Chevalley groups

## TL;DR

This paper improves the understanding of the Weyl law's remainder term for certain locally symmetric spaces associated with Chevalley groups, providing sharper estimates in the simply connected case.

## Contribution

It refines the Weyl law for spaces from simply connected Chevalley groups by establishing a power-saving estimate for the remainder term.

## Key findings

- Established a power-saving estimate for the Weyl law remainder
- Sharpened previous results by Lindenstrauss--Venkatesh
- Focused on simply connected Chevalley groups

## Abstract

Let $X$ be a locally symmetric space defined by a simple Chevalley group $G$ and a congruence subgroup of $G(\mathbb Q)$. In this generality, the Weyl law for $X$ was proved by Lindenstrauss--Venkatesh. In the case where $G$ is simply connected, we sharpen their result by giving a power saving estimate for the remainder term.