Necessary conditions for reversed Dickson polynomials of the second kind to be permutational

Shaofang Hong; Xiaoer Qin

Necessary conditions for reversed Dickson polynomials of the second kind to be permutational

Number Theory 2014-04-09 v1

Authors: Shaofang Hong , Xiaoer Qin

Abstract

In this paper, we present several necessary conditions for the reversed Dickson polynomial $E_{n}(1, x)$ of the second kind to be a permutation of $\mathbb{F}_{q}$ . In particular, we give explicit evaluation of the sum $\sum_{a\in \mathbb{F}_{q}}E_{n}(1,a)$ .

Keywords

reversed Dickson polynomials permutation polynomials finite fields character sums necessary conditions

Cite

@article{arxiv.1404.2127,
  title  = {Necessary conditions for reversed Dickson polynomials of the second kind to be permutational},
  author = {Shaofang Hong and Xiaoer Qin},
  journal= {arXiv preprint arXiv:1404.2127},
  year   = {2014}
}

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13 pages

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