Metric Diophantine approximation for systems of linear forms via dynamics

Details Metric Diophantine approximation for systems of linear forms via dynamics Metric Diophantine approximation for systems of linear forms via dynamics

2009-04-17

arxiv.org/abs/0904.2795v2

Int. J. Number Theory 6 (2010), no. 5, 1139-1168

Mathematics

Number Theory

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

Scientific paper

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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