{
  "id": "1107.0197",
  "version": "v2",
  "published": "2011-07-01T11:34:38.000Z",
  "updated": "2011-11-01T22:00:14.000Z",
  "title": "On the distribution of cubic exponential sums",
  "authors": [
    "Benoit Louvel"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using the theory of metaplectic forms,we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estimates on average over arithmetic progressions are obtained. In the second part of the paper, we prove that the sign of cubic exponential sums changes infinitely often, as the modulus runs over almost prime integers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-01T22:00:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L20",
      "11L05"
    ],
    "keywords": [
      "distribution",
      "cubic exponential sums changes",
      "asymptotic behavior",
      "metaplectic forms",
      "eisenstein integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0197L"
    }
  }
}