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arXiv · 2501.10584

On the dimension theory of Okamoto's function

Balázs Bárány·R. Dániel Prokaj
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Abstract

In this paper, we investigate the dimension theory of the one parameter family of Okamoto's function. We compute the Hausdorff, box-counting and Assouad dimensions of the graph for a typical choice of parameter. Furthermore, we study the dimension of the level sets. We give an upper bound on the dimension of every level set, and we show that for a typical choice of parameters this value is attained for Lebesgue almost every level sets.

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Balázs Bárány, R. Dániel Prokaj. 2025-01-17. On the dimension theory of Okamoto's function. https://arxiv.org/abs/2501.10584

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