GENERATION OF CLASS FIELDS BY SIEGEL-RAMACHANDRA INVARIANTS

被引：0
作者：
Shin, Dong Hwa [1 ]
机构：
[1] Hankuk Univ Foreign Studies, Dept Math, Yongin 449791, South Korea
来源：
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2015年 / 52卷 / 05期
关键词：
class field theory; complex multiplication; class numbers; elliptic and modular units; modular and automorphic functions; CLASS-NUMBER;
D O I：
10.4134/JKMS.2015.52.5.907
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show in many cases that the Siegel-Ramachandra invariants generate the ray class fields over imaginary quadratic fields. As its application we revisit the class number one problem done by Heegner and Stark, and present a new proof by making use of inequality argument together with Shimura's reciprocity law.
引用
收藏
页码：907 / 928
页数：22
相关论文
共 50 条
  • [21] Construction of Class Fields Over Imaginary Biquadratic Fields
    Koo, Ja Kyung
    Yoon, Dong Sung
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2019, 68 (02) : 413 - 434
  • [22] CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS USING y-COORDINATES OF ELLIPTIC CURVES
    Koo, Ja Kyung
    Shin, Dong Hwa
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2013, 50 (04) : 847 - 864
  • [23] Form class groups for extended ring class fields
    Koo, Ja Kyung
    Shin, Dong Hwa
    Yoon, Dong Sung
    JOURNAL OF NUMBER THEORY, 2019, 197 : 13 - 36
  • [24] Class groups of real cyclotomic fields
    Mishra, Mohit
    Schoof, Rene
    Washington, Lawrence C.
    MONATSHEFTE FUR MATHEMATIK, 2021, 195 (03): : 489 - 496
  • [25] Ring class fields and a result of Hasse
    Evans, Ron
    Lemmermeyer, Franz
    Sun, Zhi-Hong
    Van Veen, Mark
    JOURNAL OF NUMBER THEORY, 2025, 266 : 33 - 61
  • [26] INFINITE GLOBAL FIELDS AND THE GENERALIZED BRAUER-SIEGEL THEOREM
    Tsfasman, M. A.
    Vladut, S. G.
    MOSCOW MATHEMATICAL JOURNAL, 2002, 2 (02) : 329 - 402
  • [27] On the Ono invariants of imaginary quadratic number fields
    Louboutin, Stephane R.
    JOURNAL OF NUMBER THEORY, 2009, 129 (10) : 2289 - 2294
  • [28] Form Class Groups and Class Fields of CM-Fields
    Ho Yun Jung
    Ja Kyung Koo
    Dong Hwa Shin
    Dong Sung Yoon
    Results in Mathematics, 2023, 78
  • [29] Form Class Groups and Class Fields of CM-Fields
    Jung, Ho Yun
    Koo, Ja Kyung
    Shin, Dong Hwa
    Yoon, Dong Sung
    RESULTS IN MATHEMATICS, 2023, 78 (01)
  • [30] Modularity of Galois traces of ray class invariants
    Ho Yun Jung
    Chang Heon Kim
    The Ramanujan Journal, 2021, 54 : 355 - 383
12345