On the independence of greedy expansions of certain algebraic numbers in a Pisot or Salem base

IF 0.5 4区数学 Q3 MATHEMATICS

Lithuanian Mathematical Journal Pub Date : 2024-09-03 DOI:10.1007/s10986-024-09643-1

Eiji Miyanohara

引用次数: 0

Abstract

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.

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论皮索特或萨利姆基中某些代数数贪婪展开的独立性

设 β 是 β > 1 的皮索特数或萨伦数，设 α1 和 α2 是 \({\mathbb{Q}}\)(β) ∩ [0, 1) 中的元素。在本注中，我们将证明 α1 和 α2 要么在基数 β 中具有相同的尾部贪心展开，要么在基数 β 中具有独立的随机贪心展开。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lithuanian Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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.