Continued fractions with large prime partial quotients

Journal of Mathematical Analysis and Applications 2026 Open access

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Authors: Gerardo González Robert, Mumtaz Hussain, Benjamin Ward, Lauren M. White
DOI: 10.1016/j.jmaa.2026.130827
Cited by: 0

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 Łuczak (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{ü}ller (2023).

Fields of Study & Subjects

Advanced Topology and Set Theory Rings Modules and Algebras Analytic Number Theory Research

Publication details

Journal / source
Journal of Mathematical Analysis and Applications
Volume
563
Issue
2
Pages
130827–130827
Publication date
26 May 2026
Language
EN