On a class of diagonal equations over finite fields

被引：4
|
作者：
Baoulina, Ioulia N. [1 ]
机构：
[1] Moscow State Pedag Univ, Dept Math, Krasnoprudnaya Str 14, Moscow 107140, Russia
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2016年 / 40卷
关键词：
Equation over a finite field; Diagonal equation; Gauss sum; Jacobi sum; NUMBER;
D O I：
10.1016/j.ffa.2016.04.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Using properties of Gauss and Jacobi sums, we derive explicit formulas for the number of solutions to a diagonal equation of the form x(1)(2m) + ... + x(n)(2m) = 0 over a finite field of characteristic p +/- 3 (mod 8). All of the evaluations are effected in terms of parameters occurring in quadratic partitions of some powers of p. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：201 / 223
页数：23
相关论文
共 50 条
  • [1] On diagonal equations over finite fields
    Oliveira, Jose Alves
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2021, 76
  • [2] On diagonal equations over finite fields
    Luo, JG
    Sun, Q
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2001, 7 (01) : 189 - 196
  • [3] On certain diagonal equations over finite fields
    Hou, Xiang-Dong
    Sze, Christopher
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (06) : 633 - 643
  • [4] DIAGONAL EQUATIONS OVER LARGE FINITE-FIELDS
    SMALL, C
    [J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1984, 36 (02): : 249 - 262
  • [5] ZEROS OF DIAGONAL EQUATIONS OVER FINITE-FIELDS
    WAN, DQ
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (04) : 1049 - 1052
  • [6] ON THE NUMBER OF SOLUTIONS TO CERTAIN DIAGONAL EQUATIONS OVER FINITE FIELDS
    Baoulina, Ioulia
    [J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (01) : 1 - 14
  • [7] On the number of solutions of certain diagonal equations over finite fields
    Cao, Xiwang
    Chou, Wun-Seng
    Gu, Jingjing
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2016, 42 : 225 - 252
  • [8] On Solving Systems of Diagonal Polynomial Equations Over Finite Fields
    Ivanyos, Gabor
    Santha, Miklos
    [J]. FRONTIERS IN ALGORITHMICS (FAW 2015), 2015, 9130 : 125 - 137
  • [9] A note on some diagonal cubic equations over finite fields
    Ge, Wenxu
    Li, Weiping
    Wang, Tianze
    [J]. AIMS MATHEMATICS, 2024, 9 (08): : 21656 - 21671
  • [10] The number of solutions of diagonal cubic equations over finite fields
    Ge, Wenxu
    Li, Weiping
    Wang, Tianze
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2022, 80
12345