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arXiv · 0904.2795

Metric Diophantine approximation for systems of linear forms via dynamics

Dmitry Kleinbock·Gregory Margulis·Junbo Wang
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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 ${\bold R}^n$. The proofs are based on generalized quantitative nondivergence estimates for translates of measures on the space of lattices.

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Dmitry Kleinbock, Gregory Margulis, Junbo Wang. 2009-07-31. Metric Diophantine approximation for systems of linear forms via dynamics. https://arxiv.org/abs/0904.2795

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