Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields

作     者：HU Shuangnian WANG Shihan LI Yanyan NIU Yujun HU Shuangnian;WANG Shihan;LI Yanyan;NIU Yujun

作者机构：School of Mathematics and PhysicsNanyang Institute of TechnologyNanyang 473004HenanChina Faculty of Science and TechnologyBeijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519087GuangdongChina School of Information EngineeringNanyang Institute of TechnologyNanyang 473004HenanChina 

出 版 物：《Wuhan University Journal of Natural Sciences》 (武汉大学学报（自然科学英文版）)

年 卷 期：2023年第28卷第5期

页      面：369-372页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the Natural Science Foundation of Henan Province(232300420123) the National Natural Science Foundation of China(12026224) the Research Center of Mathematics and Applied Mathematics,Nanyang Institute of Technology 

主　　题：finite field rational point diagonal equations Jacobi sums 

摘      要：Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive *** F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x_(1)^(3)+x_(2)^(3)+…+x_(n)^(3)=c over Fqis given,where c∈F_(q)^(*)and p≡1(mod 3).This extends earlier results.