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math.NT2024
Borel-Cantelli, zero-one laws and inhomogeneous Duffin-Schaeffer
Victor Beresnevich, Manuel Hauke, Sanju Velani
The most versatile version of the classical divergence Borel-Cantelli lemma shows that for any divergent sequence of events in a probability space satisfying a quasi-independ…
math.NT2024
Proving the Duffin-Schaeffer conjecture without GCD graphs
Manuel Hauke, Santiago Vazquez Saez, Aled Walker
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 breakthroug…