Vaaler's theorem in number fields

Abstract

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.