Reversed Dickson polynomials of the fourth kind over finite fields

Abstract

In this paper, we obtain several results on the permutational behavior of the reversed Dickson polynomial $D_{n,3}(1,x)$ of the fourth kind over the finite field ${\mathbb{F}}_q$. Particularly, we present the explicit evaluation of the first moment ${\sum }_{a\in {\mathbb{F}}_q}{D}_{n,3}(1,a)$.

16 pages