Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group

详细信息    查看全文

• 作者：Elliot Benjamin ^{ben496@prexar.com}
• 关键词：11R29
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：173
• 期：Complete
• 页码：529-546
• 全文大小：447 K
• 卷排序：173

文摘

Let k be a real quadratic number field with 2-class group C2(k)C2(k) isomorphic to Z/2mZxZ/2nZ, m≥1m≥1, n≥2n≥2, and let k1k1 be the Hilbert 2-class field of k. We give complete criteria for C2(k1)C2(k1) to be cyclic when either dkdk, the discriminant of k, is divisible by only positive prime discriminants, or when the 2-class number of k1k1 is greater than 2, and partial criteria for C2(k1)C2(k1) to be elementary cyclic when dkdk is divisible by a negative prime discriminant.