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arXiv · 2507.17167

Continued fractions with large prime partial quotients

Gerardo González Robert·Mumtaz Hussain·Benjamin Ward·Lauren White
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Abstract

We determine the Lebesgue measure and Hausdorff dimension of various sets of real numbers with infinitely many partial quotients that are both large and prime, thus extending the well-known theorems by {\L}uczak (1997) and Huang-Wu-Xu (2020). To this end, we obtain new asymptotics on the tail end of the almost prime zeta function. Our results include some recent work by Schindler-Zweim{\"u}ller (2023).

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Gerardo González Robert, Mumtaz Hussain, Benjamin Ward, Lauren White. 2025-07-23. Continued fractions with large prime partial quotients. https://arxiv.org/abs/2507.17167

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