{
  "id": "1104.0201",
  "version": "v1",
  "published": "2011-04-01T15:38:25.000Z",
  "updated": "2011-04-01T15:38:25.000Z",
  "title": "Third Power of the Reversed Dickson Polynomial over Finite Fields",
  "authors": [
    "Xiang-dong Hou"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $D_n(1,x)$ be the $n$th reversed Dickson polynomial. The power sums $\\sum_{a\\in\\Bbb F_q}D_n(1,a)^i$, $i=1,2$, have been determined recently. In this paper we give an evaluation of the sum $\\sum_{a\\in\\Bbb F_q}D_n(1,a)^3$. This result implies new necessary conditions for $D_n(1,x)$ to be a permutation polynomial over $\\Bbb F_q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-01T15:38:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06"
    ],
    "keywords": [
      "third power",
      "finite fields",
      "th reversed dickson polynomial",
      "permutation polynomial",
      "necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0201H"
    }
  }
}