2 papers
math.NT2026
Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture
Manuel Hauke-Treuer, James Maynard, Andrew Pollington
The Duffin-Schaeffer Conjecture, proven in 2020, gives a zero-full dichotomy for the approximation of irrational numbers with reduced fractions for arbitrary approximation function…
math.NT2026
The inhomogeneous Khintchine Theorem in dimension two
Demi Allen, Manuel Hauke-Treuer, Felipe A. Ramírez
We prove that the inhomogeneous variant of Khintchine's Theorem holds in dimension without any monotonicity assumption. This resolves the last remaining case in the metric theo…