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

Fuente: arXiv
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Main Authors: Bugeaud, Yann, Kim, Dong Han
Format: Preprint
Published: 2025
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author Bugeaud, Yann
Kim, Dong Han
author_facet Bugeaud, Yann
Kim, Dong Han
contents Let $b \ge 2$ be an integer and $ξ$ an irrational real number. We establishes that, if the irrationality exponent of $ξ$ is less than $2.324 \ldots$, 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].
format Preprint
id arxiv_https___arxiv_org_abs_2510_02059
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the $b$-ary expansion of a real number whose irrationality exponent is close to 2
Bugeaud, Yann
Kim, Dong Han
Number Theory
11A63, 11J82, 68R15
Let $b \ge 2$ be an integer and $ξ$ an irrational real number. We establishes that, if the irrationality exponent of $ξ$ is less than $2.324 \ldots$, 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].
title On the $b$-ary expansion of a real number whose irrationality exponent is close to 2
topic Number Theory
11A63, 11J82, 68R15
url https://arxiv.org/abs/2510.02059