English

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 Rn{\bold R}^n. The proofs are based on generalized quantitative nondivergence estimates for translates of measures on the space of lattices.

Keywords

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

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