Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists

Details Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists

2012-02-18

arxiv.org/abs/1202.4109v1

Mathematics

Number Theory

13 pages

Scientific paper

We show that the set of numbers with bounded L\"uroth expansions (or bounded L\"uroth series) is winning and strong winning. From either winning property, it immediately follows that the set is dense, has full Hausdorff dimension, and satisfies a countable intersection property. Our result matches the well-known analogous result for bounded continued fraction expansions or, equivalently, badly approximable numbers.

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