Necessary conditions for reversed Dickson polynomials of the second kind to be permutational

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• 作者：Shaofang Hong^a ; ^b ; ^{sfhong@scu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{s-f.hong@tom.com" class="auth_mail" title="E-mail the corresponding author} ; ^{hongsf02@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Xiaoer Qin^a ; ^c ; ^{qincn328@sina.com" class="auth_mail" title="E-mail the corresponding author} ; Wei Zhao^a ; ^b ; ^{zhaowei9801@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11T06 ; 11T55 ; 11C08
• 刊名：Finite Fields and Their Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：37
• 期：Complete
• 页码：54-71
• 全文大小：347 K

文摘

In this paper, we present several necessary conditions for the reversed Dickson polynomial E_n(1,x)$E_n(1,x)$ of the second kind to be a permutation of F_q${\mathbb{F}}_q$. In particular, we give explicit evaluation of the sum ∑_a∈FqE_n(1,a)${\sum }_{a\in {\mathbb{F}}_q}{E}_n(1,a)$.