Analytic properties of representation zeta functions of groups of type ${\mathsf{A}}_2$

Abstract

We study analytic properties of the representation zeta functions of arithmetic groups of type ${\mathsf{A}}_2$, such as ${\text{SL}}_3(\mathbb{Z})$. In particular, we uncover further poles of these functions and determine a natural boundary for their meromorphic continuation beyond their abscissa of convergence. We analyse both the number field and function field case.

16 pages