Vaaler's theorem in number fields

Matthew Palmer

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arXiv · 2210.17064

Vaaler's theorem in number fields

Matthew Palmer

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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.

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Matthew Palmer. 2022-10-31. Vaaler's theorem in number fields. https://arxiv.org/abs/2210.17064

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