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Vaaler's theorem in number fields

Number Theory 2022-11-01 v1

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.

Keywords

Cite

@article{arxiv.2210.17064,
  title  = {Vaaler's theorem in number fields},
  author = {Matthew Palmer},
  journal= {arXiv preprint arXiv:2210.17064},
  year   = {2022}
}

Comments

24 pages

R2 v1 2026-06-28T04:49:10.327Z