收稿日期: 2002-02-28
修回日期: 2002-05-28
网络出版日期: 2003-03-10
Unit Group of Algebraic Real Quadratic Function Fields
Received date: 2002-02-28
Revised date: 2002-05-28
Online published: 2003-03-10
Supported by
supported by the NNSFC(No.19771052)
王鲲鹏 , 张贤科 . 实二次代数函数域的单位群(英文)[J]. 中国科学院大学学报, 2003 , 20(2) : 139 -145 . DOI: 10.7523/j.issn.2095-6134.2003.2.002
For general real quadratic algebraic function field K, a theorem on the fundamental unit ε of K is given; and for sixteen types of four series of quadratic function fields K, the fundamental unit ε is exhibited explicitly.
Key words： quadratic function field; fundamental unit; continued fraction
[1] Artin E. Quadratische Krper in Gebiete der hheren Kongruenzen Ⅰ,Ⅱ. Math Z, 1924, 19:153~206; 207~246
[2] Goss D. Basic structures of function field arithmetic. New York: Springer-Verlag, Berlin Heidelberg,1991
[3] Zhang Xian-Ke. On algebraic function fields of type(2,2,…,2). Science in China (A), 1988, 1:8~16
[4] Bernstein L. Fundamental units and cycles in the period of real quadratic number fields Ⅰ,Ⅱ.Pac J Math, 1976, 63: 37~78
[5] Levesqus C. Continued fraction expansions and fundamental units. J Math Phy Sci, 1988,22:11~44
[6] Lu Hong-Wen. Gauss′ Conjectures on the Quadratic Number Fields. Shanghai: Shanghai Sci Tech Pub, 1991
[7] Yamamoto Y. Real quadratic number fields with large fundamental units. Osaka J Math, 1971, 8: 261~270
[8] Wang Kun-Peng, Zhang Xian-Ke. Continued fractions connected with algebraic quadratic function fields.(to appear)
/
| 〈 |
|
〉 |
