{
  "id": "1804.07397",
  "version": "v1",
  "published": "2018-04-19T23:02:42.000Z",
  "updated": "2018-04-19T23:02:42.000Z",
  "title": "Supercharacters, elliptic curves, and the sixth moment of Kloosterman sums",
  "authors": [
    "Stephan Ramon Garcia",
    "George Todd"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We connect the sixth moment of Kloosterman sums to elliptic curves and provide an elementary proof that Kloosterman sums $K_u$ with $p\\nmid u$ are $O(p^{2/3})$. In particular, we can break the $O(p^{3/4})$ barrier without deep tools.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-19T23:02:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kloosterman sums",
      "elliptic curves",
      "sixth moment",
      "supercharacters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}