Analytic properties of bivariate representation and conjugacy class zeta functions of finitely generated nilpotent groups

2018/07/15 by Paula Macedo Lins de Araujo, de Araujo, Paula Macedo Lins
Computer Science · Mathematics · #11M32 #11M41 #20E45 #20F18 #22E55 #32D15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:11M32 #msc:11M41 #msc:20E45 #msc:20F18 #msc:22E55 #msc:32D15

paper · pdf · doi:10.48550/arxiv.1807.05577

20 pages

arxiv created 2018/07/15 · openalex publication_date 2018/07/15 · arxiv updated 2018/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a unipotent group scheme defined in terms of a nilpotent Lie lattice over the ring O of integers of a number field. We consider bivariate zeta functions of groups of the form G(O) encoding, respectively, the numbers of isomorphism classes of irreducible complex representations of finite dimensions and the numbers of conjugacy classes of congruence quotients of the associated groups. We show that the domains of convergence and meromorphic continuation of these zeta functions of groups G(O) are independent of the number field O considered, up to finitely many local factors.

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