{
  "id": "0904.4005",
  "version": "v2",
  "published": "2009-04-25T23:36:36.000Z",
  "updated": "2009-10-02T15:11:44.000Z",
  "title": "Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2)",
  "authors": [
    "Abhishek Saha"
  ],
  "comment": "45 pages; Some notational changes made, inaccuracies eliminated and typos fixed in accordance with an anonymous referee's helpful comments. To appear in the Pacific Journal of Mathematics",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let F be a genus two Siegel newform and g a classical newform, both of squarefree levels and of equal weight l. We prove a pullback formula for certain Eisenstein series -- thus generalizing a construction of Shimura -- and use this to derive an explicit integral representation for the degree eight L-function L(s, F X g). This integral representation involves the pullback of a simple Siegel-type Eisenstein series on the unitary group GU(3,3). As an application, we prove a reciprocity law -- predicted by Deligne's conjecture -- for the critical special values L(m, F X g) where m is an integer, 2 <= m <= l/2-1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-02T15:11:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F67",
      "11F70"
    ],
    "keywords": [
      "critical l-values",
      "simple siegel-type eisenstein series",
      "unitary group gu",
      "explicit integral representation",
      "reciprocity law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.4005S"
    }
  }
}