{
  "id": "1201.3515",
  "version": "v2",
  "published": "2012-01-17T14:06:40.000Z",
  "updated": "2012-07-18T14:47:25.000Z",
  "title": "The Saito-Kurokawa lifting and Darmon points",
  "authors": [
    "Matteo Longo",
    "Marc-Hubert Nicole"
  ],
  "comment": "14 pages. Title changed",
  "doi": "10.1007/s00208-012-0846-5",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E_{/_\\Q}$ be an elliptic curve of conductor $Np$ with $p\\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\\infty$ the $p$-adic Hida family passing though $f$, and by $F_\\infty$ its $\\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\\{\\widetilde A_T(k)\\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-18T14:47:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F32",
      "11F46",
      "11F85"
    ],
    "keywords": [
      "darmon points",
      "fourier coefficients",
      "siegel modular forms admits",
      "positive definite symmetric half-integral matrices",
      "adic saito-kurokawa lift"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}