Theoretical study demonstrates a new proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation, highlighting an improved error-term.
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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Hauke et al. (2024) studied this question.
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