四川大学学报（自然科学版）2024，Vol.61Issue(2)：13-18,6.DOI:10.19907/j.0490-6756.2024.021001
有限域上一类四次对角方程有理点的个数
The number of solutions of certain quartic diagonal equations over finite field
摘要
Abstract
Let p be a prime,k be a positive integer and Fq be the finite field of q= pk elements.Let F*q be the multiplicative group of Fq,that is,F*q=Fq\{0}.For a polynomial f(x1,…,xn)over Fq,use N(f(x1,…,xn)=0)to denote the number of solutions of f(x1,x2,…,xn)=0 over Fq.In 1981,Myerson gave a formula for N(x41 +⋯+ x4n=0).Recently,Zhao and coworkers obtained the explicit formulas for N(x41 + x42 = c),N(x41 + x42 + x43 = c)and N(x41 + x42 + x43 + x44 = c),where c∈ F*q.In this paper,by using the Jacobi sums and an analog of the Hasse-Davenport theorem,we obtain the exact formula for N(x41 +⋯+ x4n= c)and thus extend the known results.关键词
有限域/有理点/对角方程/雅可比和Key words
Finite field/Rational point/Diagonal equation/Jacobi sum分类
数理科学引用本文复制引用
胡双年,高继东,杜屹洋..有限域上一类四次对角方程有理点的个数[J].四川大学学报（自然科学版）,2024,61(2):13-18,6.基金项目
国家自然科学基金(12026224) （12026224）
河南省自然科学基金(232300420123) （232300420123）
