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.
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