English

On geometry of simultaneous approximation to three real numbers

Number Theory 2024-01-18 v2

Abstract

Considering simultaneous approximation to three numbers, we study the geometry of the sequence of best approximations. We provide a sharper lower bound for the ratio between ordinary and uniform exponent of Diophantine approximation, optimal in terms of this geometry.

Keywords

Cite

@article{arxiv.2203.04242,
  title  = {On geometry of simultaneous approximation to three real numbers},
  author = {Antoine Marnat and Nikolay Moshchevitin},
  journal= {arXiv preprint arXiv:2203.04242},
  year   = {2024}
}

Comments

15 pages, 2 figures

R2 v1 2026-06-24T10:06:19.961Z