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":"1 1","pages":""},"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\":\"1 1\",\"pages\":\"\"},\"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}
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.