由 Thue-Morse 的平方和立方子序列生成的实数的线性独立性

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-02-29 DOI:10.1007/s10474-024-01417-y

E. Miyanohara

引用次数: 0

摘要

让 \((t(m))_{m \ge0}\) 是 Thue-Morse 序列，并且 \(b>2\) 是整数。本文将证明实数 \(1)、\(sum_{m=0}^\infty {\frac{t(m^2)}{{b}^{m+1}}\) 和 \(sum_{m=0}^\infty {\frac{t(m^3)}{{b}^{m+1}}\) 在 \(\mathbb{Q}\)上是线性独立的。）

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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Linear independence of the real numbers generated by the square and cube subsequences of Thue–Morse

Let \((t(m))_{m \ge0}\) be Thue-Morse sequence and \(b>2\) be an integer. In this paper, we prove that the real numbers \(1\), \(\sum_{m=0}^\infty {\frac{t(m^2)}{{b}^{m+1}}}\) and \(\sum_{m=0}^\infty {\frac{t(m^3)}{{b}^{m+1}}}\) are linearly independent over \(\mathbb{Q}\).

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.