{
  "id": "1410.7892",
  "version": "v1",
  "published": "2014-10-29T07:48:54.000Z",
  "updated": "2014-10-29T07:48:54.000Z",
  "title": "Kloosterman paths and the shape of exponential sums",
  "authors": [
    "Emmanuel Kowalski",
    "William F. Sawin"
  ],
  "comment": "27 pages, 3 figures",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums, as their parameter varies modulo a prime tending to infinity. Using independence of Kloosterman sheaves, we prove convergence in the sense of finite distributions to a specific random Fourier series. We also consider Birch sums, for which we can establish convergence in law in the space of continuous functions. We then derive some applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-29T07:48:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T23",
      "11L05",
      "14F20",
      "60F17",
      "60G17",
      "60G50"
    ],
    "keywords": [
      "exponential sums",
      "kloosterman paths",
      "polygonal paths joining partial sums",
      "specific random fourier series",
      "parameter varies modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7892K"
    }
  }
}