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Third Power of the Reversed Dickson Polynomial over Finite Fields

By Xiang-dong Hou


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 $\Bbb F_q$.Comment: 17 page

Topics: Mathematics - Combinatorics, 11T06
Year: 2011
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