English

The $p$-adic Duffin--Schaeffer conjecture

Number Theory 2022-05-11 v2

Abstract

We prove Haynes' version of the Duffin--Schaeffer conjecture for the pp-adic numbers. In addition, we prove several results about an associated related but false conjecture, related to pp-adic approximation in the spirit of Jarn\'ik and Lutz.

Keywords

Cite

@article{arxiv.2110.02598,
  title  = {The $p$-adic Duffin--Schaeffer conjecture},
  author = {Simon Kristensen and Mathias Løkkegaard Laursen},
  journal= {arXiv preprint arXiv:2110.02598},
  year   = {2022}
}

Comments

Typos corrected and clarifications made, following suggestions of a referee

R2 v1 2026-06-24T06:39:46.133Z