{
  "id": "1209.1894",
  "version": "v4",
  "published": "2012-09-10T07:34:03.000Z",
  "updated": "2014-10-14T20:05:31.000Z",
  "title": "Double Dirichlet series and quantum unique ergodicity of weight 1/2 Eisenstein series",
  "authors": [
    "Yiannis N. Petridis",
    "Nicole Raulf",
    "Morten S. Risager"
  ],
  "comment": "45 pages, 4 figures. Several minor corrections. To appear in Algebra and Number theory",
  "categories": [
    "math.NT",
    "math.SP"
  ],
  "abstract": "The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for {\\Gamma}_0(4) leads to the study of certain double Dirichlet series involving GL2 automorphic forms and Dirichlet characters. We study the analytic properties of this family of double Dirichlet series (analytic continuation, convexity estimate) and prove that a subconvex estimate implies the QUE result.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-02-10T08:09:21.000Z",
      "abstract": "The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for {\\Gamma}_0(4) leads to the study of certain double Dirichlet series involving GL2 automorphic forms and Dirichlet characters. We study the analytic properties of this family of double Dirichlet series (analytic continuation, convexity estimate) and prove that a subconvex estimate with saving of the order {\\delta} > 1/8 implies the QUE result.",
      "comment": "45 pages, 4 figures. Changed definition of subconvexity for multiple Dirichlet series. Added explanation why convexity doesn't follow directly from Maass-Selberg",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-10-14T20:05:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J51",
      "11F68",
      "11F72"
    ],
    "keywords": [
      "double dirichlet series",
      "quantum unique ergodicity",
      "eisenstein series",
      "gl2 automorphic forms",
      "dirichlet characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.1894P"
    }
  }
}