arXiv 2103.005442021-03math.NT

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

Bo Tan, Baowei Wang, Jun Wu

英文摘要：

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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