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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

OAI identifier:
oai:arXiv.org:1104.0201

Provided by:
arXiv.org e-Print Archive

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