{
  "id": "0803.1870",
  "version": "v3",
  "published": "2008-03-12T23:05:58.000Z",
  "updated": "2009-02-17T00:45:06.000Z",
  "title": "Non-vanishing of the symmetric square $L$-function at the central point",
  "authors": [
    "Rizwanur Khan"
  ],
  "comment": "29 pages",
  "doi": "10.1112/plms/pdp048",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using the mollifier method, we show that for a positive proportion of holomorphic Hecke eigenforms of level one and weight bounded by a large enough constant, the associated symmetric square $L$-function does not vanish at the central point of its critical strip. We note that our proportion is the same as that found by other authors for other families of $L$-functions also having symplectic symmetry type.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-02-17T00:45:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M99"
    ],
    "keywords": [
      "central point",
      "holomorphic hecke eigenforms",
      "symplectic symmetry type",
      "mollifier method",
      "non-vanishing"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1870K"
    }
  }
}