Vaaler's theorem in number fields

In Diophantine approximation, Vaaler’s theorem was an important partial result towards the Duffin–Schaeffer conjecture, which was open for almost eighty years before it was recently proven by Koukoulopoulos and Maynard. A version of this result was previously proven to also hold in imaginary quadratic fields: in this paper, we establish a version of Vaaler’s theorem in general number fields.