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arXiv · 2609.30921

Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture

Manuel Hauke-Treuer·James Maynard·Andrew Pollington
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Abstract

The Duffin-Schaeffer Conjecture, proven in 2020, gives a zero-full dichotomy for the approximation of irrational numbers with reduced fractions for arbitrary approximation functions. We construct approximation functions such that the inhomogeneous analogue of the Duffin-Schaeffer Conjecture fails. The counterexamples are obtained for all non-zero rationals and certain Liouville numbers.

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BibTeXRIS

Manuel Hauke-Treuer, James Maynard, Andrew Pollington. 2026-09-25. Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture. https://arxiv.org/abs/2609.30921

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