{"title":"Normal integral bases of Lehmer’s cyclic quintic fields","authors":"Yu Hashimoto, Miho Aoki","doi":"10.1007/s11139-024-00875-w","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(K_n\\)</span> be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer’s parametric polynomial. We give all normal integral bases for <span>\\(K_n\\)</span> only by the roots of the polynomial, which is a generalization of the work of Lehmer in the case that <span>\\(n^4+5n^3+15n^2+25n+25\\)</span> is prime number, and Spearman–Willliams in the case that <span>\\(n^4+5n^3+15n^2+25n+25\\)</span> is square free.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"55 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-05","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/s11139-024-00875-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let \(K_n\) be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer’s parametric polynomial. We give all normal integral bases for \(K_n\) only by the roots of the polynomial, which is a generalization of the work of Lehmer in the case that \(n^4+5n^3+15n^2+25n+25\) is prime number, and Spearman–Willliams in the case that \(n^4+5n^3+15n^2+25n+25\) is square free.
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