On the number of solutions of two-variable diagonal quartic equations over finite fields

被引：7
|
作者：
Zhao, Junyong [1 ,2 ]
Zhao, Yang [3 ]
Niu, Yujun [1 ]
机构：
[1] Nanyang Inst Thchnol, Sch Math & Stat, Nanyang 473004, Peoples R China
[2] Sichuan Univ, Math Coll, Chengdu 610064, Peoples R China
[3] Nanyang Normal Univ, Nanyang 473061, Peoples R China
来源：
AIMS MATHEMATICS | 2020年 / 5卷 / 04期
关键词：
diagonal hypersurface; rational point; finite field; Gauss sum; Jacobi sum; EXPONENTIAL-SUMS; NEWTON POLYGONS; RATIONAL-POINTS; POLYNOMIALS; HYPERSURFACES; ZEROS;
D O I：
10.3934/math.2020192
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let p be a odd prime number and let F-q be the finite field of characteristic p with q elements. In this paper, by using the Gauss sum and Jacobi sum, we give an explicit formula for the number N(x(1)(4) + x(2)(4) = c) of solutions of the following two-variable diagonal quartic equations over F-q: x(1)(4) + x(2)(4) = c with c is an element of F-q*. From this result, one can deduce that N(x(1)(4) + x(2)(4) = c) = q + O(q(1/2)).
引用
收藏
页码：2979 / 2991
页数：13
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