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arXiv · 2509.13254

Analytic properties of representation zeta functions of groups of type $\mathsf{A_2}$

Valentin Blomer·Christopher Voll
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Abstract

We study analytic properties of the representation zeta functions of arithmetic groups of type $\mathsf{A}_2$, such as $\textrm{SL}_3(\mathbb{Z})$. 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.

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Valentin Blomer, Christopher Voll. 2025-09-16. Analytic properties of representation zeta functions of groups of type $\mathsf{A_2}$. https://arxiv.org/abs/2509.13254

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