Permutational behavior of reversed Dickson polynomials over finite fields

AIMS Mathematics

Kaimin Cheng¹ 

关键词: : ;    Permutation polynomial;    Reversed Dickson polynomial of the (k + 1)-th kind;    Finite field;    Generating function;   

DOI  :  10.3934/Math.2017.2.244

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

In this paper, we develop the method presented previouslyby Hong, Qin and Zhao to obtain several results on the permutationalbehavior 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 thefirst moment $\sum_{a\in {\mathbb F}_{q}}D_{n,k}(1,a)$.Our results extend the results of Hong, Qin and Zhaoto the general $k\ge 0$ case.

【 授权许可】

CC BY