The Duffin-Schaeffer Conjecture with extra divergence II

TL;DR

This paper advances the proof of the Duffin-Schaeffer Conjecture by establishing its validity under an additional divergence condition, bringing us closer to resolving the conjecture for measures near Lebesgue.

Contribution

It introduces an 'extra divergence' hypothesis that, when satisfied, guarantees the truth of the Duffin-Schaeffer Conjecture, extending previous partial results.

Findings

Proves the conjecture under the new divergence condition

Shows the conjecture holds for measures close to Lebesgue

Provides a new approach to the conjecture's proof

Abstract

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.