Mahler's question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory
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 3adic expansion, a complete metric theory for this variant intrinsic Diophantine approximation is presented which yields the divergence theory of Mahler's original question.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 arXiv:
 arXiv:2103.00544
 Bibcode:
 2021arXiv210300544T
 Keywords:

 Mathematics  Number Theory;
 11J83;
 11K55