On the remainder term of the Weyl law for congruence subgroups of 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.

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