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

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Permutational behavior of reversed Dickson polynomials over finite fields

Kaimin Cheng

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

Received: , Accepted: , Published:

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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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6. X. Qin, G. Qian and S. Hong, New results on permutation polynomials over finite fields, Int. J. Number Theory, 11 (2015), 437-449.

7. Q. Wang and J. L. Yucas, Dickson polynomials over finite fields, Finite Fields Appl., 18 (2012), 814-831.

Copyright Info: © 2017, Kaimin Cheng, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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