CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS USING y-COORDINATES OF ELLIPTIC CURVES

被引：1

作者：

Koo, Ja Kyung ^{[1
]}

Shin, Dong Hwa ^{[2
]}

机构：

[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 3731, South Korea

[2] Hankuk Univ Foreign Studies, Dept Math, Gyeonggi Do 449791, South Korea

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2013年 / 50卷 / 04期

关键词：

class field theory; complex multiplication; elliptic and modular units; modular functions;

D O I：

10.4134/JKMS.2013.50.4.847

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By a change of variables we obtain new y-coordinates of elliptic curves. Utilizing these y-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the y-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

引用

页码：847 / 864

页数：18

共 14 条

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