Metric Diophantine approximation for systems of linear forms via dynamics
Number Theory
2011-06-10 v2 Dynamical Systems
Abstract
The goal of this paper is to generalize the main results of [KM] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish `joint strong extremality' of arbitrary finite collection of smooth nondegenerate submanifolds of . The proofs are based on generalized quantitative nondivergence estimates for translates of measures on the space of lattices.
Cite
@article{arxiv.0904.2795,
title = {Metric Diophantine approximation for systems of linear forms via dynamics},
author = {Dmitry Kleinbock and Gregory Margulis and Junbo Wang},
journal= {arXiv preprint arXiv:0904.2795},
year = {2011}
}
Comments
27 pages; minor corrections made. To appear in Int. J. Number Theory