Diophantine approximation for products of linear maps—logarithmic improvements

Gorodnik, Alexander; Vishe, Pankaj

doi:10.1090/tran/6953

Diophantine approximation for products of linear maps—logarithmic improvements

Gorodnik, Alexander; Vishe, Pankaj

Authors

Alexander Gorodnik

Dr Pankaj Vishe pankaj.vishe@durham.ac.uk
Associate Professor

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.

Citation

Gorodnik, A., & Vishe, P. (2016). Diophantine approximation for products of linear maps—logarithmic improvements. Transactions of the American Mathematical Society, 370(1), 487-507. https://doi.org/10.1090/tran/6953

Journal Article Type	Article
Acceptance Date	Apr 16, 2016
Online Publication Date	Apr 16, 2016
Publication Date	Apr 16, 2016
Deposit Date	Apr 19, 2016
Publicly Available Date	Apr 28, 2016
Journal	Transactions of the American Mathematical Society
Print ISSN	0002-9947
Electronic ISSN	1088-6850
Publisher	American Mathematical Society
Peer Reviewed	Peer Reviewed
Volume	370
Issue	1
Pages	487-507
DOI	https://doi.org/10.1090/tran/6953

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Copyright Statement
© 2016 American Mathematical Society. First published in Transactions of the American Mathematical Society in (April 2016), published by the American Mathematical Society.