Normal bases of ray class fields over imaginary quadratic fields

被引：8

作者：

Jung, Ho Yun ^{[1
]}

Koo, Ja Kyung ^{[1
]}

Shin, Dong Hwa ^{[1
]}

机构：

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

来源：

MATHEMATISCHE ZEITSCHRIFT | 2012年 / 271卷 / 1-2期

关键词：

Class fields; Modular functions; Normal bases;

D O I：

10.1007/s00209-011-0854-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop a criterion for a normal basis (Theorem 2.4), and prove that the singular values of certain Siegel functions form normal bases of ray class fields over imaginary quadratic fields other than Q(root-1) and Q(root-3) (Theorem 4.2). This result would be an answer for the Lang-Schertz conjecture on a ray class field with modulus generated by an integer (>= 2) (Remark 4.3).

引用

页码：109 / 116

页数：8

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