The Duffin-Schaeffer conjecture with extra divergence
Christoph Aistleitner, Thomas Lachmann, Marc Munsch, Niclas Technau,, and Agamemnon Zafeiropoulos

TL;DR
This paper proves the Duffin-Schaeffer conjecture under an additional divergence condition, advancing understanding in metric number theory and solving a previously posed open problem.
Contribution
It establishes the conjecture's validity when the divergence persists after dividing the approximation function by a logarithmic factor.
Findings
Proves the Duffin-Schaeffer conjecture with extra divergence condition.
Improves upon previous results by relaxing divergence requirements.
Solves a problem posed by Haynes, Pollington, and Velani.
Abstract
The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. It asserts that for every non-negative function for almost all reals there are infinitely many coprime solutions to the inequality , provided that the series is divergent. In the present paper we prove that the conjecture is true under the "extra divergence" assumption that divergence of the series still holds when is replaced by for some . This improves a result of Beresnevich, Harman, Haynes and Velani, and solves a problem posed by Haynes, Pollington and Velani.
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