用韦伯函数生成以2、3、4或6为模的射线类场

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Korean Mathematical Society Pub Date : 2018-01-01 DOI:10.4134/JKMS.J170220

H. Jung, J. Koo, D. Shin

{"title":"用韦伯函数生成以2、3、4或6为模的射线类场","authors":"H. Jung, J. Koo, D. Shin","doi":"10.4134/JKMS.J170220","DOIUrl":null,"url":null,"abstract":". Let K be an imaginary quadratic ﬁeld with ring of integers O K . Let E be an elliptic curve with complex multiplication by O K , and let h E be the Weber function on E . Let N ∈ { 2 , 3 , 4 , 6 } . We show that h E alone when evaluated at a certain N -torsion point on E generates the ray class ﬁeld of K modulo N O K . This would be a partial answer to the question raised by Hasse and Ramachandra.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Generation of ray class fields modulo 2, 3, 4 or 6 by using the Weber function\",\"authors\":\"H. Jung, J. Koo, D. Shin\",\"doi\":\"10.4134/JKMS.J170220\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let K be an imaginary quadratic ﬁeld with ring of integers O K . Let E be an elliptic curve with complex multiplication by O K , and let h E be the Weber function on E . Let N ∈ { 2 , 3 , 4 , 6 } . We show that h E alone when evaluated at a certain N -torsion point on E generates the ray class ﬁeld of K modulo N O K . This would be a partial answer to the question raised by Hasse and Ramachandra.\",\"PeriodicalId\":49993,\"journal\":{\"name\":\"Journal of the Korean Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/JKMS.J170220\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J170220","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 7

摘要

．设K是一个由整数O K组成的环的虚二次域。设E是一条椭圆曲线与O K的复数相乘，设E是E上的韦伯函数。设N∈{2,3,4,6}。我们证明了E在E上某个N -扭转点处单独求值会产生K模N O K的射线类场。这将是对Hasse和Ramachandra提出的问题的部分回答。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Generation of ray class fields modulo 2, 3, 4 or 6 by using the Weber function

. Let K be an imaginary quadratic ﬁeld with ring of integers O K . Let E be an elliptic curve with complex multiplication by O K , and let h E be the Weber function on E . Let N ∈ { 2 , 3 , 4 , 6 } . We show that h E alone when evaluated at a certain N -torsion point on E generates the ray class ﬁeld of K modulo N O K . This would be a partial answer to the question raised by Hasse and Ramachandra.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the Korean Mathematical Society 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).