{
  "id": "1111.5455",
  "version": "v3",
  "published": "2011-11-23T11:00:52.000Z",
  "updated": "2016-03-18T22:41:35.000Z",
  "title": "Asymptotic behaviors of Kloosterman sums",
  "authors": [
    "Ping Xi"
  ],
  "comment": "This paper has been withdrawn by the author because there is a gap in Lemma 9",
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper has been withdrawn by the author because there is a gap in Lemma 9.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-01T01:33:31.000Z",
      "abstract": "By virtue of Chebyshev polynomials and the Rademacher-Menchov device, we investigate the asymptotic behaviors of Kloosterman sums over short intervals by making use of the Gallagher-Montgomery refinement on D.A. Burgess' estimate for character sums, and an estimate analogous of N.M. Katz's Sate-Tate law is obtained. Subsequently, we can gain some information on the sign changes and extreme values of Kloosterman sums.",
      "comment": "20 pages, Lemma 9 and some other minor errors have been revised",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-03-18T22:41:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05"
    ],
    "keywords": [
      "kloosterman sums",
      "asymptotic behaviors",
      "katzs sate-tate law",
      "short intervals",
      "extreme values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5455X"
    }
  }
}