Analytic properties of representation zeta functions of groups of type A₂

2025/09/16 by Blomer, Valentin, Voll, Christopher
#11M41 #20G35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.13254

Abstract

We study analytic properties of the representation zeta functions of arithmetic groups of type A₂, such as \textrmSL₃(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.

Citations

• Explicit Analytic Continuation of Euler Products
• Representation zeta functions of groups of type A₂ in positive characteristic
• Uniform analytic properties of representation zeta functions of finitely\n generated nilpotent groups
• Arithmetic groups, base change, and representation growth
• Representation Growth for Linear Groups

Related

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• Rationality of representation zeta functions of compact p-adic\n analytic groups
• On representation zeta functions for special linear groups