{
  "id": "1706.01391",
  "version": "v1",
  "published": "2017-06-05T16:05:42.000Z",
  "updated": "2017-06-05T16:05:42.000Z",
  "title": "Reversed Dickson polynomials of the $(k+1)$-th kind over Finite Fields, II",
  "authors": [
    "Neranga Fernando"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be an odd prime and $q$ a power of $p$. The properties and the permutation behavior of the reversed Dickson polynomials of the $(k+1)$-th kind $D_{n,k}(1,x)$ over finite fields have been an interesting topic as shown in the predecessor of the present paper. In this paper, we explain the permutation behaviour of $D_{n,k}(1,x)$ when $n=p^{l_1}+3$, $n=p^{l_1}+p^{l_2}+p^{l_3}$, and $n=p^{l_1}+p^{l_2}+p^{l_3}+p^{l_4}$, where $l_1, l_2$, $l_3$, and $l_4$ are non-negative integers. A generalization $n=p^{l_1}+p^{l_2}+\\cdots +p^{l_i}$ is also explained. We also present some algebraic and arithmetic properties of the reversed Dickson polynomials of the $(k+1)$-th kind $D_{n,k}(1,x)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-05T16:05:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11T55"
    ],
    "keywords": [
      "reversed dickson polynomials",
      "th kind",
      "finite fields",
      "permutation behaviour",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}