标题： 三阶逆Dickson多项式在有限域上 显示英文标题

标题： Third Power of the Reversed Dickson Polynomial over Finite Fields

摘要： 设$D_n(1,x)$为第$n$个反转迪克森多项式。 幂和$\sum_{a\in\Bbb F_q}D_n(1,a)^i$,$i=1,2$最近已被确定。 在本文中，我们给出了求和$\sum_{a\in\Bbb F_q}D_n(1,a)^3$的计算结果。 这个结果意味着对于$D_n(1,x)$在$\Bbb F_q$上成为置换多项式的新的必要条件。 显示英文摘要

摘要： Let $D_n(1,x)$ be the $n$th reversed Dickson polynomial. The power sums $\sum_{a\in\Bbb F_q}D_n(1,a)^i$, $i=1,2$, have been determined recently. In this paper we give an evaluation of the sum $\sum_{a\in\Bbb F_q}D_n(1,a)^3$. This result implies new necessary conditions for $D_n(1,x)$ to be a permutation polynomial over $\Bbb F_q$.