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arXiv · 2512.11357

Asymptotic statistics for finite continued fractions with restricted digits

Jungwon Lee
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Abstract

Zaremba's conjecture concerns a formation of continued fraction expansions for rational numbers with partial quotient bounded by an absolute constant. We present asymptotic estimates for the size of $\epsilon$-thickening of certain fractal sets of bounded-type, which in turn provide a remark on Zaremba's conjecture in an averaging sense. We also discuss a generalisation for complex continued fractions over imaginary quadratic fields.

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Jungwon Lee. 2025-12-12. Asymptotic statistics for finite continued fractions with restricted digits. https://arxiv.org/abs/2512.11357

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