Alternating geometric progressions modulo one and Sturmian words

2026/03/23 by Qing Lu, Weizhe Zheng
#math.NT #math.CO

paper · pdf

Abstract

Let b≥ 2 be an integer. Using Sturmian words we describe all irrational real numbers ξ such that the image in ℝ/ℤ of the sequence (ξ(-b)ⁿ)_{n≥ 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.

Citations

• Symbolic Dynamics II. Sturmian Trajectories

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