Intrinsic Approximation on Cantor-like Sets, a Problem of Mahler

Details Intrinsic Approximation on Cantor-like Sets, a Problem of Mahler Intrinsic Approximation on Cantor-like Sets, a Problem of Mahler

2011-06-02

arxiv.org/abs/1106.0526v2

Mathematics

Number Theory

7 pages, 0 figures

Scientific paper

In 1984, Kurt Mahler posed the following fundamental question: How well can irrationals in the Cantor set be approximated by rationals in the Cantor set? Towards development of such a theory, we prove a Dirichlet-type theorem for this intrinsic diophantine approximation on Cantor-like sets, and discuss related possible theorems/conjectures. The resulting approximation function is analogous to that for R^d, but with d being the Hausdorff dimension of the set, and logarithmic dependence on the denominator instead.

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