{
  "id": "math/0108054",
  "version": "v1",
  "published": "2001-08-08T01:11:45.000Z",
  "updated": "2001-08-08T01:11:45.000Z",
  "title": "On the exceptional zeros of Rankin-Selberg L-functions",
  "authors": [
    "Dinakar Ramakrishnan",
    "Song Wang"
  ],
  "comment": "31 pages. For ps, dvi and pdf formats of the paper, see http://www.math.caltech.edu/people/dinakar.html",
  "categories": [
    "math.NT"
  ],
  "abstract": "The main objects of study in this article are two classes of Rankin-Selberg L-unctions, namely L(s, f \\times g) and L(s, sym^2(g) \\times sym^2(g)), where f, g are newforms, holomorphic or of Maass type, on the upper half plane, and sym^2(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any Landau-Siegel zeros. These zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound on the norm of sym^2(g).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-08-08T01:11:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F66",
      "11F55",
      "11F80"
    ],
    "keywords": [
      "rankin-selberg l-functions",
      "exceptional zeros",
      "upper half plane",
      "symmetric square lift",
      "strong lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......8054R"
    }
  }
}