The Duffin-Schaeffer Conjecture with extra divergence

Alan Haynes, Andrew Pollington, Sanju Velani

Given a nonnegative function $\psi :\mathbb{N}\to \mathbb{R}$, let $W(\psi )$ denote the set of real numbers $x$ such that $|nx-a|<\psi (n)$ for infinitely many reduced rationals $a/n(n>0)$. A conseq…