{
  "id": "1007.4732",
  "version": "v2",
  "published": "2010-07-27T14:25:34.000Z",
  "updated": "2010-07-30T12:02:13.000Z",
  "title": "Prime density results for Hecke eigenvalues of a Siegel cusp form",
  "authors": [
    "Abhishek Saha"
  ],
  "comment": "8 pages. Minor changes made over previous version. To appear in Int. J. Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let F in S_k(Sp(2g, Z)) be a cuspidal Siegel eigenform of genus g with normalized Hecke eigenvalues mu_F(n). Suppose that the associated automorphic representation pi_F is locally tempered everywhere. For each c>0 we consider the set of primes p for which |mu_F(p)| >= c and we provide an explicit upper bound on the density of this set. In the case g=2, we also provide an explicit upper bound on the density of the set of primes p for which mu_F(p) >= c.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-30T12:02:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F66",
      "11F70",
      "22E50"
    ],
    "keywords": [
      "siegel cusp form",
      "prime density results",
      "explicit upper bound",
      "cuspidal siegel eigenform",
      "normalized hecke eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4732S"
    }
  }
}