The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. It asserts that for every non-negative function ψ:N→R for almost all reals x there are infinitely many coprime solutions (a,n) to the inequality |nx−a|0. This improves a result of Beresnevich, Harman, Haynes and Velani, and solves a problem posed by Haynes, Pollington and Velani.
The Duffin-Schaeffer conjecture with extra divergence
Munsch M.;
2019-01-01
Abstract
The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. It asserts that for every non-negative function ψ:N→R for almost all reals x there are infinitely many coprime solutions (a,n) to the inequality |nx−a|0. This improves a result of Beresnevich, Harman, Haynes and Velani, and solves a problem posed by Haynes, Pollington and Velani.
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