高斯和与有理点的计算
PDF下载 (227)姜 坤,高 伟,曹 炜.高斯和与有理点的计算[J].宁波大学学报(理工版),2020,33(1):65-68.DOI:
JIANG Kun,GAO Wei,CAO Wei.Gauss sums and computation of rational points[J].Journal of Ningbo University(Natural Science & Engineering Edition),2020,33(1):65-68.DOI:
| Title: | Gauss sums and computation of rational points |
| 作者: | 姜 坤, 高 伟, 曹 炜 |
| Author(s): | JIANG Kun, GAO Wei, CAO Wei |
| 关键词: | 有限域; 有理点; 高斯和; 特征 |
| Keywords: | finite field; rational point; Gauss sum; character |
| 分类号: | O156.1 |
| 文献标识码: | A |
| 摘要: | 计算有限域上代数簇有理点个数是有限域研究中的重要课题. 设为q元有限域, f是上的非零多项式, Df为其次数矩阵, 用N(f)表示超曲面f=0在上的有理点个数. 若Df在剩余类环中与整数矩阵A行等价, 则记为Df ~qA. 利用高斯和给出了当Df ~q diag(), 其中∈{1, p1}, p1为q-1的一个素因子时N(f) 的具体表达式, 从而推广了已知的结论. |
| Abstract: | It is important in the area of finite fields study to compute the number of rational points on algebraic varieties in finite fields. Let be the finite field of order q and f be a nonzero polynomial over with degree matrix Df; denote by N(f) the number of -rational points of the hypersurface defined by f=0; write Df ~qA when Df is row equivalent to an integer matrix A in the residue ring . Using Gauss sums, we obtain the explicit formula for N(f) in the case of Df ~q diag(), where and p1 is a prime divisor of q-1, which generalizes the known results. |
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| 备注/Memo: | 收稿日期: 2019－06－22. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11871291）; 宁波市自然科学基金（2019A610035）. 第一作者: 姜坤（1997－）, 女, 山东梁山人, 在读硕士研究生, 主要研究方向: 数论. E-mail: 718044618@qq.com *通信作者: 曹炜（1974－）, 男, 湖北潜江人, 博士/教授, 主要研究方向: 数论与密码学. E-mail: caowei@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
