{
  "id": "1102.1872",
  "version": "v5",
  "published": "2011-02-09T14:27:09.000Z",
  "updated": "2013-12-26T19:32:03.000Z",
  "title": "On some arithmetic properties of automorphic forms of GL(m) over a division algebra",
  "authors": [
    "H. Grobner",
    "A. Raghuram"
  ],
  "comment": "The paper has been revised once more before publication and its DOI has been added",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "In this paper we investigate arithmetic properties of automorphic forms on the group G' = GL_m/D, for a central division-algebra D over an arbitrary number field F. The results of this article are generalizations of results in the split case, i.e., D=F, by Shimura, Harder, Waldspurger and Clozel for square-integrable automorphic forms and also by Franke and Franke-Schwermer for general automorphic representations. We also compare our theorems on automorphic forms of the group G' to statements on automorphic forms of its split form using the global Jacquet-Langlands correspondence developed by Badulescu and Badulescu-Renard. Beside that we prove that the local version of the Jacquet-Langlands transfer at an archimedean place preserves the property of being cohomological.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-12-26T19:32:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F75",
      "22E47",
      "11F67"
    ],
    "keywords": [
      "arithmetic properties",
      "division algebra",
      "arbitrary number field",
      "general automorphic representations",
      "global jacquet-langlands correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.1872G"
    }
  }
}