{
  "id": "1605.05240",
  "version": "v1",
  "published": "2016-05-17T17:09:22.000Z",
  "updated": "2016-05-17T17:09:22.000Z",
  "title": "Permutational behavior of reversed Dickson polynomials over finite fields",
  "authors": [
    "Kaimin Cheng"
  ],
  "comment": "16 pages. arXiv admin note: substantial text overlap with arXiv:1604.04557",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we use the method developed previously by Hong, Qin and Zhao to obtain several results on the permutational behavior of the reversed Dickson polynomial $D_{n,k}(1,x)$ of the $(k+1)$-th kind over the finite field ${\\mathbb F}_{q}$. Particularly, we present the explicit evaluation of the first moment $\\sum_{a\\in {\\mathbb F}_{q}}D_{n,k}(1,a)$. Our results extend the known results from the case $0\\le k\\le 3$ to the general $k\\ge 0$ case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-17T17:09:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reversed dickson polynomial",
      "permutational behavior",
      "finite field",
      "th kind",
      "explicit evaluation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}