Permutational behavior of reversed Dickson polynomials over finite fields
Kaimin Cheng · AIMS Mathematics · 2017
In this paper, we develop the method presented 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 results of Hong, Qin and Zhao to the general $k\ge 0$ case.