Abstract:Let $b\ge 2$ be an integer. Using Sturmian words we describe all irrational real numbers $\xi$ such that the image in $\mathbb{R}/\mathbb{Z}$ of the sequence $(\xi (-b)^n)_{n\ge 0}$ is contained in an interval of length $b^{-1}+b^{-2}-b^{-3}$. In previous work (arXiv:2603.16794) we showed that the image cannot be contained in a shorter interval.
From: Weizhe Zheng [view email]
[v1]
Mon, 23 Mar 2026 14:46:59 UTC (13 KB)
[v2]
Thu, 2 Apr 2026 08:33:34 UTC (13 KB)
[v3]
Thu, 23 Jul 2026 13:53:34 UTC (13 KB)
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