{"title":"论皮索特或萨利姆基中某些代数数贪婪展开的独立性","authors":"Eiji Miyanohara","doi":"10.1007/s10986-024-09643-1","DOIUrl":null,"url":null,"abstract":"<p>Let <i>β</i> be a Pisot or Salem number with <i>β ></i> 1, and let <i>α</i><sub>1</sub> and <i>α</i><sub>2</sub> be elements in <span>\\({\\mathbb{Q}}\\)</span>(<i>β</i>) ∩ [0<i>,</i> 1). In this note, we prove that <i>α</i><sub>1</sub> and <i>α</i><sub>2</sub> have either the same tail greedy expansions in a base <i>β</i> or independent random greedy expansions in a base <i>β</i>.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"40 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the independence of greedy expansions of certain algebraic numbers in a Pisot or Salem base\",\"authors\":\"Eiji Miyanohara\",\"doi\":\"10.1007/s10986-024-09643-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>β</i> be a Pisot or Salem number with <i>β ></i> 1, and let <i>α</i><sub>1</sub> and <i>α</i><sub>2</sub> be elements in <span>\\\\({\\\\mathbb{Q}}\\\\)</span>(<i>β</i>) ∩ [0<i>,</i> 1). In this note, we prove that <i>α</i><sub>1</sub> and <i>α</i><sub>2</sub> have either the same tail greedy expansions in a base <i>β</i> or independent random greedy expansions in a base <i>β</i>.</p>\",\"PeriodicalId\":51108,\"journal\":{\"name\":\"Lithuanian Mathematical Journal\",\"volume\":\"40 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lithuanian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10986-024-09643-1\",\"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":"Lithuanian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10986-024-09643-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the independence of greedy expansions of certain algebraic numbers in a Pisot or Salem base
Let β be a Pisot or Salem number with β > 1, and let α1 and α2 be elements in \({\mathbb{Q}}\)(β) ∩ [0, 1). In this note, we prove that α1 and α2 have either the same tail greedy expansions in a base β or independent random greedy expansions in a base β.
期刊介绍：
The Lithuanian Mathematical Journal publishes high-quality original papers mainly in pure mathematics. This multidisciplinary quarterly provides mathematicians and researchers in other areas of science with a peer-reviewed forum for the exchange of vital ideas in the field of mathematics.
The scope of the journal includes but is not limited to:
Probability theory and statistics;
Differential equations (theory and numerical methods);
Number theory;
Financial and actuarial mathematics, econometrics.
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