Alexander Gorodnik
Diophantine approximation for products of linear maps—logarithmic improvements
Gorodnik, Alexander; Vishe, Pankaj
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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Accepted Journal Article
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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.
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