有限域上逆Dickson多项式的三次幂
Third Power of the Reversed Dickson Polynomial over Finite Fields
摘要：
设$D_n(1,x)$为第$n$次逆Dickson多项式。最近已经确定了幂和$\sum_{a\in\Bbb F_q}D_n(1,a)^i$、$i=1,2$。本文给出了和$\sum_{a\in\Bbb F_q}D_n(1,a)^3$的一个估计.这个结果暗示了$D_n(1,x)$是$\Bbb F_q$上置换多项式的新的必要条件。
英文摘要：
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 $\Bbb F_q$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
