Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers
Number Theory
2021-03-15 v2
Abstract
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a result by Haynes, Jensen and Kristensen. Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington, Velani, Zafeiropoulos and Zorin.
Keywords
Cite
@article{arxiv.2103.03605,
title = {Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers},
author = {Sam Chow and Agamemnon Zafeiropoulos},
journal= {arXiv preprint arXiv:2103.03605},
year = {2021}
}
Comments
This generalises the previous version