文献类型：期刊文献

英文题名：The number of solutions of diagonal cubic equations over finite fields

作者：Ge, Wenxu[1];Li, Weiping[2];Wang, Tianze[1]

第一作者：Ge, Wenxu

通讯作者：Ge, WX[1]

机构：[1]North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R China;[2]Henan Univ Econ & Law, Sch Math & Informat Sci, Zhengzhou 450046, Peoples R China

第一机构：North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R China

通讯机构：[1]corresponding author), North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450046, Peoples R China.

年份：2022

卷号：80

外文期刊名：FINITE FIELDS AND THEIR APPLICATIONS

收录：;EI(收录号：20220811703376);Scopus(收录号：2-s2.0-85125019163);WOS:【SCI-EXPANDED(收录号:WOS:000807822000007)】；

基金：Acknowledgments The authors are partially supported by the National Natural Science Foundation of China (Grant No. 11871193, 12071132) and the Natural Science Foundation of Henan Province (No. 202300410031, 222300420493) .

语种：英文

外文关键词：Gauss sum; Jacobi sum; Generating function; Diagonal cubic equation; Exponential sum

摘要：Let Fq be a finite field of q = pk elements. For any z & ISIN; Fq, let An(z) and Bn(z) denote the number of solutions of the equations x31 + x32 + & BULL; & BULL; & BULL; + x3n = z and x31 + x32 + & BULL; & BULL; & BULL; + x3n + zx3n+1 = 0 respectively. Recently, using the generator of Fq*, Hong and Zhu gave the generating functions E & INFIN; and E & INFIN;n=1 An(z)xn n=1 Bn(z)xn. In this paper, we give the generating functions E & INFIN;n=1 An(z)xn and E & INFIN;n=1 Bn(z)xn immediately by the coefficient z. Moreover, we gave the formulas of the number of solutions of equation a1x31 + a2x32 + a3x33 = 0 and our formulas are immediately determined by the coefficients a1, a2 and a3. These extend and improve earlier results. (c) 2022 Elsevier Inc. All rights reserved.