  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.

Number Theory