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

Valentin Blomer; Christopher Voll

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

Number Theory 2025-09-17 v1

Authors: Valentin Blomer , Christopher Voll

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.

Keywords

representation zeta function arithmetic group meromorphic continuation natural boundary SL_3(Z)

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@article{arxiv.2509.13254,
  title  = {Analytic properties of representation zeta functions of groups of type $\mathsf{A_2}$},
  author = {Valentin Blomer and Christopher Voll},
  journal= {arXiv preprint arXiv:2509.13254},
  year   = {2025}
}

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16 pages

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

Abstract

Keywords

Cite

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