{
  "id": "math/0502470",
  "version": "v1",
  "published": "2005-02-23T09:02:25.000Z",
  "updated": "2005-02-23T09:02:25.000Z",
  "title": "Real zeros and size of Rankin-Selberg L-functions in the level aspect",
  "authors": [
    "Guillaume Ricotta"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, some asymptotic formulas are proved for the harmonic mollified second moment of a family of Rankin-Selberg L-functions. One of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method on average. A first consequence is a new subconvexity bound for Rankin-Selberg L-functions in the level aspect. Moreover, infinitely many Rankin-Selberg L-functions having at most eight non-trivial real zeros are produced and some new non-trivial estimates for the analytic rank of the family studied are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-23T09:02:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41"
    ],
    "keywords": [
      "rankin-selberg l-functions",
      "level aspect",
      "harmonic mollified second moment",
      "non-trivial real zeros",
      "analytic rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2470R"
    }
  }
}