Metric Diophantine approximation for systems of linear forms via dynamics

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

27 pages; minor corrections made. To appear in Int. J. Number Theory

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