{
  "id": "math/0606578",
  "version": "v1",
  "published": "2006-06-23T04:19:46.000Z",
  "updated": "2006-06-23T04:19:46.000Z",
  "title": "Shimura correspondence for level p^2 and the central values of L-series",
  "authors": [
    "Ariel Pacetti",
    "Gonzalo Tornaría"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a weight 2 and level p^2 modular form f, we construct two weight 3/2 modular forms (possibly zero) of level 4p^2 and non trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imaginary quadratic twists of f. Furthermore, we give a general framework for our construction that applies to any order in definite quaternion algebras, with which one can, in principle, construct weight 3/2 modular forms of any level, provided one knows how to compute ideal classes representatives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-23T04:19:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F37",
      "11F67"
    ],
    "keywords": [
      "central value",
      "shimura correspondence",
      "modular form",
      "imaginary quadratic twists",
      "non trivial character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6578P"
    }
  }
}