{
  "id": "1602.04545",
  "version": "v1",
  "published": "2016-02-15T02:05:52.000Z",
  "updated": "2016-02-15T02:05:52.000Z",
  "title": "Reversed Dickson Polynomials of the Third Kind",
  "authors": [
    "Neranga Fernando"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime and $q=p^e$. We discuss the properties of the reversed Dickson polynomial $D_{n,2}(1,x)$ of the third kind. We also give several necessary conditions for the reversed Dickson polynomial of the third kind $D_{n,2}(1,x)$ to be a permutation of $\\mathbb{F}_{q}$. In particular, we give explicit evaluation of the sum $\\sum_{a\\in \\mathbb{F}_q}D_{n,2}(1,a)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-15T02:05:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11T55",
      "11C08"
    ],
    "keywords": [
      "reversed dickson polynomial",
      "third kind",
      "necessary conditions",
      "explicit evaluation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204545F"
    }
  }
}