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Diophantine approximation for products of linear maps—logarithmic improvements.

Gorodnik, Alexander and Vishe, Pankaj (2016) 'Diophantine approximation for products of linear maps—logarithmic improvements.', Transactions of the American Mathematical Society., 370 (1). pp. 487-507.

Abstract

This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of this product become arbitrary close to zero, and we establish that, in fact, they approximate zero with an explicit rate. Our approach is based on investigating quantitative density of orbits of higher-rank abelian groups.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1090/tran/6953
Publisher statement:© 2016 American Mathematical Society. First published in Transactions of the American Mathematical Society in (April 2016), published by the American Mathematical Society.
Record Created:27 Apr 2016 16:50
Last Modified:01 Nov 2017 09:27

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