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

@inproceedings{Tan2021MahlersQF, title={Mahler's question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory}, author={Bo Tan and Bao-Wei Wang and Jun Wu}, year={2021} }

In this paper, we consider the intrinsic Diophantine approximation on the triadic Cantor set K, i.e. approximating the points in K by rational numbers inside K, a question posed by K. Mahler. By using another height function of a rational number in 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.

## One Citation

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