On the b-ary expansion of a real number whose irrationality exponent is close to 2

2025/10/02 by Yann Bugeaud, Bugeaud, Yann, Dong Han Kim +1 · 1 citation
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2510.02059

Abstract

Let b ≥ 2 be an integer and ξ an irrational real number. We establishes that, if the irrationality exponent of ξ is less than 2.324 …, then the b-ary expansion of ξ cannot be `too simple', in a suitable sense. This improves the results of our previous paper [Ann. Sc. Norm. Super. Pisa Cl. Sci., 2017].

Citations

• A new complexity function, repetitions in Sturmian words, and irrationality exponents of Sturmian numbers

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