F. Hörmann, Antonella Perucca, Pietro Sgobba, S. Tronto
{"title":"EXPLICIT KUMMER THEORY FOR QUADRATIC FIELDS","authors":"F. Hörmann, Antonella Perucca, Pietro Sgobba, S. Tronto","doi":"10.17654/NT050020151","DOIUrl":null,"url":null,"abstract":"LetK be a quadratic number field and let α ∈ K. We present an explicit finite procedure to compute at once all Kummer degrees [K(ζm, n √ α) : K(ζm)] for n,m > 1 with n | m, where ζm denotes a primitive m-th root of unity. We can also replace α by any finitely generated subgroup of K×.","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"1 1","pages":"151-178"},"PeriodicalIF":0.2000,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"JP Journal of Algebra Number Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/NT050020151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
LetK be a quadratic number field and let α ∈ K. We present an explicit finite procedure to compute at once all Kummer degrees [K(ζm, n √ α) : K(ζm)] for n,m > 1 with n | m, where ζm denotes a primitive m-th root of unity. We can also replace α by any finitely generated subgroup of K×.
期刊介绍：
The JP Journal of Algebra, Number Theory and Applications is a peer-reviewed international journal. Original research papers theoretical, computational or applied, in nature, in any branch of Algebra and Number Theory are considered by the JPANTA. Together with the core topics in these fields along with their interplay, the journal promotes contributions in Diophantine equations, Representation theory, and Cryptography. Realising the need of wide range of information for any emerging area of potential research, the journal encourages the submission of related survey articles as well.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
