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arXiv · 2108.13287

On the rational approximation to Thue--Morse rational numbers

Yann Bugeaud·Guo-Niu Han
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Abstract

Let $b \ge 2$ and $\ell \ge 1$ be integers. We establish that there is an absolute real number $K$ such that all the partial quotients of the rational number $$ \prod_{h = 0}^\ell \, (1 - b^{-2^h}), $$ of denominator $b^{2^{\ell+1} - 1}$, do not exceed $\exp(K (\log b)^2 \sqrt{\ell} 2^{\ell/2})$.

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Yann Bugeaud, Guo-Niu Han. 2021-08-30. On the rational approximation to Thue--Morse rational numbers. https://arxiv.org/abs/2108.13287

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