{
  "id": "1804.02352",
  "version": "v2",
  "published": "2018-04-06T16:49:17.000Z",
  "updated": "2018-08-05T09:07:14.000Z",
  "title": "Pullbacks of Saito--Kurokawa lifts and a central value formula",
  "authors": [
    "Aprameyo Pal",
    "Carlos de Vera-Piquero"
  ],
  "comment": "64 pages, typos and minor issues corrected",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an explicit central value formula for a family of complex $L$-series of degree $6$ for $\\mathrm{GL}_2 \\times \\mathrm{GL}_3$ which arise as factors of certain Garret--Rankin triple product $L$-series associated with modular forms. Our result generalizes a previous formula of Ichino involving Saito--Kurokawa lifts, and as an application, we prove Deligne's conjecture stating the algebraicity of the central values of the considered $L$-series up to the relevant periods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-08-05T09:07:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F32",
      "11F67"
    ],
    "keywords": [
      "saito-kurokawa lifts",
      "explicit central value formula",
      "garret-rankin triple product",
      "delignes conjecture",
      "result generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}