Proving the Duffin-Schaeffer conjecture without GCD graphs

2024/04/23 by Hauke, Manuel, Saez, Santiago Vazquez, Walker, Aled · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2404.15123

Abstract

We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthrough first argument, but simplifies and strengthens several technical aspects. In particular, we avoid any direct handling of GCD graphs and their `quality'. We also consider the metric quantitative theory of Diophantine approximations, improving the (log Ψ(N))^-C error-term of Aistleitner-Borda and the first named author to exp(-(log Ψ(N))^{(1)/(2) - ε}).

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