关于单位群和 $$\mathbb {Q}(\sqrt{2},\sqrt{p},\sqrt{q})$$ 的 2 级数

Mohamed Mahmoud Chems-Eddin, Moha Ben Taleb El Hamam, Moulay Ahmed Hajjami
{"title":"关于单位群和 $$\\mathbb {Q}(\\sqrt{2},\\sqrt{p},\\sqrt{q})$$ 的 2 级数","authors":"Mohamed Mahmoud Chems-Eddin, Moha Ben Taleb El Hamam, Moulay Ahmed Hajjami","doi":"10.1007/s11139-024-00947-x","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(p\\equiv 1\\pmod {8}\\)</span> and <span>\\(q\\equiv 7\\pmod 8\\)</span> be two prime numbers. The purpose of this paper is to compute the unit groups of the fields <span>\\(\\mathbb {L}=\\mathbb {Q}(\\sqrt{2}, \\sqrt{p}, \\sqrt{q})\\)</span> and give their 2-class numbers.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the unit group and the 2-class number of $$\\\\mathbb {Q}(\\\\sqrt{2},\\\\sqrt{p},\\\\sqrt{q})$$\",\"authors\":\"Mohamed Mahmoud Chems-Eddin, Moha Ben Taleb El Hamam, Moulay Ahmed Hajjami\",\"doi\":\"10.1007/s11139-024-00947-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span>\\\\(p\\\\equiv 1\\\\pmod {8}\\\\)</span> and <span>\\\\(q\\\\equiv 7\\\\pmod 8\\\\)</span> be two prime numbers. The purpose of this paper is to compute the unit groups of the fields <span>\\\\(\\\\mathbb {L}=\\\\mathbb {Q}(\\\\sqrt{2}, \\\\sqrt{p}, \\\\sqrt{q})\\\\)</span> and give their 2-class numbers.</p>\",\"PeriodicalId\":501430,\"journal\":{\"name\":\"The Ramanujan Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Ramanujan Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11139-024-00947-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00947-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

让(p(1/pmod {8})和(q(7/pmod 8)是两个素数。本文的目的是计算域 \(\mathbb {L}=\mathbb {Q}(\sqrt{2}, \sqrt{p}, \sqrt{q})\) 的单位群,并给出它们的二阶数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

On the unit group and the 2-class number of $$\mathbb {Q}(\sqrt{2},\sqrt{p},\sqrt{q})$$

On the unit group and the 2-class number of $$\mathbb {Q}(\sqrt{2},\sqrt{p},\sqrt{q})$$

Let \(p\equiv 1\pmod {8}\) and \(q\equiv 7\pmod 8\) be two prime numbers. The purpose of this paper is to compute the unit groups of the fields \(\mathbb {L}=\mathbb {Q}(\sqrt{2}, \sqrt{p}, \sqrt{q})\) and give their 2-class numbers.

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
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信