{"title":"Continued Fractions in Hyperelliptic Fields with an Arbitrarily Long Period","authors":"V. P. Platonov, G. V. Fedorov","doi":"10.1134/S1064562424701928","DOIUrl":null,"url":null,"abstract":"<p>The article proves the following statement: in any hyperelliptic field <i>L</i> defined over the field of algebraic numbers <i>K</i> which having non-trivial units of the ring of integer elements of the field <i>L</i>, there is an element for which the period length of the continued fraction is greater any pre-given number.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424701928","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
The article proves the following statement: in any hyperelliptic field L defined over the field of algebraic numbers K which having non-trivial units of the ring of integer elements of the field L, there is an element for which the period length of the continued fraction is greater any pre-given number.
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