有限域上一类方程的解数
PDF下载 (458)余杜鹃,曹 炜*.有限域上一类方程的解数[J].宁波大学学报(理工版),2013,27(01):66-69.DOI:
YU Du-juan,CAO Wei.Number of Solutions to a Class of Equations over Finite Fields[J].Journal of Ningbo University(Natural Science & Engineering Edition),2013,27(01):66-69.DOI:
| Title: | Number of Solutions to a Class of Equations over Finite Fields |
| 作者: | 余杜鹃, 曹 炜* |
| Author(s): | YU Du-juan, CAO Wei |
| 关键词: | 次数矩阵; 有效降次; 椭圆曲线; Hasse 定理 |
| Keywords: | degree matrix; effective reduction; elliptic curve; Hasses theorem |
| 分类号: | O156 |
| 文献标识码: | A |
| 摘要: | 研究有限域 上一类方程 , , 的解数. 在保持方程系数不变的前提下, 通过对其次数矩阵进行有效降次, 可以改进对原方程解数的各种估计. 若对方程未知变量和系数进行适当限定, 则可将其化为椭圆曲线方程, 从而利用Hasse定理得到原方程解数的一个精确界. |
| Abstract: | We study the number of solutions to the following equation: , , . While keeping the coefficients unchanged, we effectively reduce the degree matrix to improve the estimates on the number of solutions to the equation. Furthermore with certain constraint conditions on the variables and coefficients, we obtain a sharp bound on the number of solutions to the equation using Hasse’s theorem for elliptic curves over finite fields. |
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| 备注/Memo: | 收稿日期: 2013?04?30. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 宁波市自然科学基金（2012A610034）.第一作者: 余杜鹃（1988－）, 女, 江西上饶人, 在读硕士研究生, 主要研究方向: 数论与密码. E-mail: pinganjiankangydj@163.com*通信作者: 曹 炜（1974－）, 男, 湖北潜江人, 博士/副研究员, 主要研究方向: 数论、有限域及其应用. E-mail: caowei@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
