{
  "id": "1507.07416",
  "version": "v1",
  "published": "2015-07-27T14:38:58.000Z",
  "updated": "2015-07-27T14:38:58.000Z",
  "title": "On the Genericity of Eisenstein Series and Their Residues for Covers of $GL_m$",
  "authors": [
    "Solomon Friedberg",
    "David Ginzburg"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $\\tau_1^{(r)}$, $\\tau_2^{(r)}$ be two genuine cuspidal automorphic representations on $r$-fold covers of the adelic points of the general linear groups $GL_{n_1}$, $GL_{n_2}$, resp., and let $E(g,s)$ be the associated Eisenstein series on an $r$-fold cover of $GL_{n_1+n_2}$. Then the value or residue at any point $s=s_0$ of $E(g,s)$ is an automorphic form, and generates an automorphic representation. In this note we show that if $n_1\\neq n_2$ these automorphic representations (when not identically zero) are generic, while if $n_1=n_2:=n$ they are generic except for residues at $s=\\frac{n\\pm1}{2n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-27T14:38:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F27",
      "11F55",
      "11F70",
      "17B08"
    ],
    "keywords": [
      "genericity",
      "genuine cuspidal automorphic representations",
      "fold cover",
      "general linear groups",
      "adelic points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}