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

In this paper, we consider Mahler's question for intrinsic Diophantine approximation on the triadic Cantor set K , i.e., approximating the points in K by rational numbers inside K : W K (ψ) : = x ∈ K : | x - p / q | < ψ (q) , for infinitely many p / q ∈ K. By using the intrinsic denominator q int instead of the regular denominator q of a rational p / q ∈ K in ψ (·) , we present a complete metric theory for this variant of the set W K (ψ) , which yields a divergence theory of Mahler's question. [ABSTRACT FROM AUTHOR]