AIMS Mathematics, 2017, 2(2): 244-259. doi: 10.3934/Math.2017.2.244.

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Permutational behavior of reversed Dickson polynomials over finite fields

School of Mathematics and information, China west normal University, Nanchong 637009, P.R. China

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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.
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Citation: Kaimin Cheng. Permutational behavior of reversed Dickson polynomials over finite fields. AIMS Mathematics, 2017, 2(2): 244-259. doi: 10.3934/Math.2017.2.244

References

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