Mohamed Mahmoud Chems-Eddin, Moulay Ahmed Hajjami, Mohammed Taous
{"title":"Hilbert Genus Fields of Some Number Fields with High Degrees","authors":"Mohamed Mahmoud Chems-Eddin, Moulay Ahmed Hajjami, Mohammed Taous","doi":"10.1007/s40306-022-00489-8","DOIUrl":null,"url":null,"abstract":"<div><p>The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields <span>\\(L_{m,d}:=\\mathbb {Q}(\\zeta _{2^{m}},\\sqrt {d})\\)</span>, where <i>m</i> ≥ 3 is a positive integer and <i>d</i> is a square-free integer whose prime divisors are congruent to ± 3 (mod 8) or 9 (mod 16).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00489-8.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-022-00489-8","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: 0
Abstract
The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields \(L_{m,d}:=\mathbb {Q}(\zeta _{2^{m}},\sqrt {d})\), where m ≥ 3 is a positive integer and d is a square-free integer whose prime divisors are congruent to ± 3 (mod 8) or 9 (mod 16).
期刊介绍:
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.