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arXiv · 2103.00544

Mahler's question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory

Bo Tan·Baowei Wang·Jun Wu
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Abstract

In this paper, we consider the intrinsic Diophantine approximation on the triadic Cantor set $\mathcal{K}$, i.e. approximating the points in $\mathcal{K}$ by rational numbers inside $\mathcal{K}$, a question posed by K. Mahler. By using another height function of a rational number in $\mathcal{K}$, i.e. the denominator obtained from its periodic 3-adic expansion, a complete metric theory for this variant intrinsic Diophantine approximation is presented which yields the divergence theory of Mahler's original question.

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Bo Tan, Baowei Wang, Jun Wu. 2021-02-28. Mahler's question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory. https://arxiv.org/abs/2103.00544

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