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arXiv · 2605.26839

Lower bounds for the Hausdorff dimension of expressible sets

Maiken Gravgaard·Simon Kristensen·Jaroslav Hančl
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Abstract

We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form $\sum_{n=1}^\infty \frac{1}{a_n b_n}$, where $b_n$ satisfies some growth condition and $a_n$ lies in some set, possibly depending on $n$. As a consequence of our results, some of the irrational numbers arising from Erd\H{o}s' celebrated construction from 1976 are not Liouville numbers.

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Maiken Gravgaard, Simon Kristensen, Jaroslav Hančl. 2026-05-26. Lower bounds for the Hausdorff dimension of expressible sets. https://arxiv.org/abs/2605.26839

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