Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents
Number Theory
2019-03-28 v2
Abstract
We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine approximation on manifolds and to weighted badly approximable vectors. Finally, we interpret and prove a conjecture of Beresnevich-Velani (2010) about inhomogeneous intermediate exponents.
Keywords
Cite
@article{arxiv.1808.07184,
title = {Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents},
author = {Sam Chow and Anish Ghosh and Lifan Guan and Antoine Marnat and David Simmons},
journal= {arXiv preprint arXiv:1808.07184},
year = {2019}
}
Comments
Minor revisions following referee report. This is the final version. To appear in Annali Della Scuola Normale Superiore Di Pisa