{"title":"p-adic数域的某些完全分枝扩展的显式一致化器","authors":"Hugues Bellemare, Antonio Lei","doi":"10.1007/s12188-020-00215-x","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>p</i> be an odd prime number. We construct explicit uniformizers for the totally ramified extension <span>\\({\\mathbb {Q}}_p(\\zeta _{p^2},\\root p \\of {p})\\)</span> of the field of <i>p</i>-adic numbers <span>\\({\\mathbb {Q}}_p\\)</span>, where <span>\\(\\zeta _{p^2}\\)</span> is a primitive <span>\\(p^2\\)</span>-th root of unity.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-020-00215-x","citationCount":"2","resultStr":"{\"title\":\"Explicit uniformizers for certain totally ramified extensions of the field of p-adic numbers\",\"authors\":\"Hugues Bellemare, Antonio Lei\",\"doi\":\"10.1007/s12188-020-00215-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <i>p</i> be an odd prime number. We construct explicit uniformizers for the totally ramified extension <span>\\\\({\\\\mathbb {Q}}_p(\\\\zeta _{p^2},\\\\root p \\\\of {p})\\\\)</span> of the field of <i>p</i>-adic numbers <span>\\\\({\\\\mathbb {Q}}_p\\\\)</span>, where <span>\\\\(\\\\zeta _{p^2}\\\\)</span> is a primitive <span>\\\\(p^2\\\\)</span>-th root of unity.</p></div>\",\"PeriodicalId\":50932,\"journal\":{\"name\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s12188-020-00215-x\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12188-020-00215-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-020-00215-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Explicit uniformizers for certain totally ramified extensions of the field of p-adic numbers
Let p be an odd prime number. We construct explicit uniformizers for the totally ramified extension \({\mathbb {Q}}_p(\zeta _{p^2},\root p \of {p})\) of the field of p-adic numbers \({\mathbb {Q}}_p\), where \(\zeta _{p^2}\) is a primitive \(p^2\)-th root of unity.
期刊介绍：
The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.
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