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<p>We study analytic properties of the representation zeta functions of arithmetic groups of type <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textsf{A}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="sans-serif">A</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, such as <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textsf{SL}_3(\mathbb {Z})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="sans-serif">SL</mi> <mn>3</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. 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.</p>

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

  • 期刊论文

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  • 发表日期：

    2026年5月28日

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  • Valentin Blomer,
  • Christopher Voll

摘要

We study analytic properties of the representation zeta functions of arithmetic groups of type \(\textsf{A}_2\) A 2 , such as \(\textsf{SL}_3(\mathbb {Z})\) SL 3 ( 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.