{
  "id": "math/0410067",
  "version": "v2",
  "published": "2004-10-04T22:10:52.000Z",
  "updated": "2004-10-19T21:52:24.000Z",
  "title": "The Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations",
  "authors": [
    "Joshua S. Friedman"
  ],
  "comment": "25 pages, submitted to Mathematische Zeitschrift",
  "doi": "10.1007/s00209-005-0806-9",
  "categories": [
    "math.NT",
    "math.SP"
  ],
  "abstract": "For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of Elstrodt, Grunewald and Mennicke to non-trivial unitary representations. We show that the presence of cuspidal elliptic elements sometimes adds ramification point to the zeta function. In fact, if D is the ring of Eisenstein integers, then the Selberg zeta-function of PSL(2,D) contains ramification points and is the sixth-root of a meromorphic function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-19T21:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F72",
      "11M36"
    ],
    "keywords": [
      "selberg trace formula",
      "cofinite kleinian groups",
      "finite-dimensional unitary representations",
      "selberg zeta-function",
      "adds ramification point"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10067F"
    }
  }
}