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

Q: What type of study is this?

This is a Quantitative Study study.

Yann Bugeaud; Dong Han Kim

doi:10.48550/arxiv.2510.02059

October 2, 2025Open Access

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

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Key Points

The study finds that real numbers with irrationality exponents less than 2.324 have complex b-ary expansions.
It improves upon previous results that explored the relationship between irrationality exponent and expansion complexity.
The findings suggest limitations in how 'simple' the expansions of these numbers can be under certain conditions.
The paper provides a new insight into the characteristics of irrational numbers and their numerical representations.

Implication

Analysis reveals that b-ary expansions of irrational numbers show complexity when the irrationality exponent is below 2.324, implying deeper structure.

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].

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Cite This Study

Bugeaud et al. (2025) studied this question.

synapsesocial.com/papers/68e25559d6d66a53c2474fa2 https://doi.org/10.48550/arxiv.2510.02059

View Full Paper

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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