Duffin--Schaeffer examples, real residue systems, and Bohr-set primes

Stefan M. Hesseling, Felipe A. Ramirez

We prove the following generalization of a well-known result of Duffin and Schaeffer: For any given countable sets $Y\subset \mathbb{R}$ and $Z\subset\mathbb{R}\setminus\operatorna…