Work

Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.30921

Authors: Hauke-Treuer, Manuel, Maynard, James, Pollington, Andrew

Institution: University of Oxford

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214625913

Cites: 4

Cited by: 2

Related to: 10