{
  "id": "1807.05577",
  "version": "v1",
  "published": "2018-07-15T17:12:26.000Z",
  "updated": "2018-07-15T17:12:26.000Z",
  "title": "Analytic properties of bivariate representation and conjugacy class zeta functions of finitely generated nilpotent groups",
  "authors": [
    "Paula Macedo Lins de Araujo"
  ],
  "comment": "20 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\mathbf{G}$ be a unipotent group scheme defined in terms of a nilpotent Lie lattice over the ring $\\mathcal{O}$ of integers of a number field. We consider bivariate zeta functions of groups of the form $\\mathbf{G}(\\mathcal{O})$ 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 $\\mathbf{G}(\\mathcal{O})$ are independent of the number field $\\mathcal{O}$ considered, up to finitely many local factors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-15T17:12:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "11M32",
      "20F18",
      "32D15",
      "22E55",
      "20E45"
    ],
    "keywords": [
      "conjugacy class zeta functions",
      "finitely generated nilpotent groups",
      "analytic properties",
      "bivariate representation",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}