Permutational behavior of reversed Dickson polynomials over finite fields

Kaimin Cheng

Published 2016-05-17Version 1

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.