论整数在奥斯特洛夫斯基和递推运算系统中的表示法

arXiv - MATH - Number Theory Pub Date : 2024-09-10 DOI:arxiv-2409.06232

Mohit Mittal, Divyum Sharma

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摘要

我们提供了关于线性递推数系和奥斯特洛夫斯基-$\alpha$数系（其中$\alpha$是二次有理数）的具有有界哈明权重的正整数的有效上界。我们证明了一个整数在两个textit{different} Ostrowski数系中的表示的类似结果。

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On the representation of an integer in Ostrowski and recurrence numeration systems

We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski-$\alpha$ numeration system, where $\alpha$ is a quadratic irrational. We prove a similar result for the representation of an integer in two \textit{different} Ostrowski numeration systems.

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arXiv - MATH - Number Theory

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