费马曲线上的有理点
PDF下载 (325)徐 浪,曹 炜*.费马曲线上的有理点[J].宁波大学学报(理工版),2015,28(03):48-52.DOI:
XU Lang,CAO Wei.Rational Points on Fermat Curves over Finite Fields[J].Journal of Ningbo University(Natural Science & Engineering Edition),2015,28(03):48-52.DOI:
| Title: | Rational Points on Fermat Curves over Finite Fields |
| 作者: | 徐 浪, 曹 炜* |
| Author(s): | XU Lang, CAO Wei |
| 关键词: | 费马曲线; 有限域; 射影平面; 仿射平面; 有理点 |
| Keywords: | Fermat curves; finite fields; projective space; affine space; rational points |
| 分类号: | O156 |
| 文献标识码: | A |
| 摘要: | 当时, 给出费马曲线上有理点的具体形式及其个数公式. 当时, 给出上该费马曲线有理点个数的简单公式, 并得到了这些曲线上的有理点乘积为上立方数的充分条件. |
| Abstract: | We give an explicit description of rational points and the number of points in on the Fermat curve for . We find a simple formula of the number of rational points in on the Fermat curve for . A sufficient condition is obtained for the product to be a cube in where is the points on these curves |
| 参考文献 /References: | [1] Wolfmann J. The number of solutions of certain diagonal equations over finite fields[J]. Journal of Number Theory, 1992, 42(2):247-257. [2] Moisio M. On the number of rational points on some families of Fermat curves over finite fields[J]. Finite Fields and Their Applications, 2007, 13(3):546-562. [3] Hou X D, Sze C. On certain diagonal equations over finite fields[J]. Finite Fields and Their Applications, 2009, 15(6):633-643. [4] Voloch J F, Zieve M E. Rational points on some Fermat curves and surfaces over finite fields[J]. International Journal of Number Theory, 2014, 10(2):603-621. [5] 张禾瑞. 近世代数基础[M]. 北京: 高等教育出版社, 1978:151-174. [6] Lidl R, Niederreiter H. Finite fields[M]. Cambridge: Cambridge Univ Press, 1997:187-239. Ireland K, Rosen M. A classical introduction to modern number theory[M]. New York: Springer-verlag, 1990: 138-161. |
| 备注/Memo: | 收稿日期: 2014?12?21. 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（2014A610017）. 第一作者: 徐浪（1991－）, 女, 湖北咸宁人, 在读硕士研究生, 主要研究方向: 数论与密码. E-mail: shuxuexulang@163.com *通信作者: 曹炜（1974－）, 男, 湖北潜江人, 博士/副教授, 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/ |
