{
  "id": "0910.4303",
  "version": "v2",
  "published": "2009-10-22T12:08:44.000Z",
  "updated": "2010-02-01T14:59:26.000Z",
  "title": "Non-vanishing of Jacobi Poincaré series",
  "authors": [
    "Soumya Das"
  ],
  "comment": "15 pages; abstract updated, new results and proofs added",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that under suitable conditions, the Jacobi Poincar\\'{e} series of exponential type of integer weight and matrix index does not vanish identically. For classical Jacobi forms, we construct a basis consisting of the \"first\" few Poincar\\'{e} series and also give conditions both dependent and independent of the weight, which ensures non-vanishing of classical Jacobi Poincar\\'{e} series. Equality of certain Kloosterman-type sums is proved. Also, a result on the non-vanishing of Jacobi Poincar\\'{e} series is obtained when an odd prime divides the index.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-01T14:59:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F50"
    ],
    "keywords": [
      "non-vanishing",
      "odd prime divides",
      "integer weight",
      "classical jacobi forms",
      "matrix index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.4303D"
    }
  }
}