{"title":"具有任意长周期的超椭圆场中的连续分数","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":531,"journal":{"name":"Doklady Mathematics","volume":"109 2","pages":"147 - 151"},"PeriodicalIF":0.5000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":531,\"journal\":{\"name\":\"Doklady Mathematics\",\"volume\":\"109 2\",\"pages\":\"147 - 151\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1064562424701928\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424701928","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
摘要 文章证明了以下陈述：在代数数域 K 上定义的任何超椭圆域 L 中，如果域 L 的整数元素环上有非三维单元，则存在一个元素，其续分数的周期长度大于任何给定的数。
Continued Fractions in Hyperelliptic Fields with an Arbitrarily Long Period
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.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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