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Diophantine approximation for products of linear maps — logarithmic improvements


Gorodnik, Alexander; Vishe, Pankaj (2018). Diophantine approximation for products of linear maps — logarithmic improvements. Transactions of the American Mathematical Society, 370(1):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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics
Language:English
Date:2018
Deposited On:23 Jan 2019 12:35
Last Modified:29 Jul 2020 07:59
Publisher:American Mathematical Society
ISSN:0002-9947
Additional Information:First published inTransactions of the American Mathematical Society in 370 (2018), published by the American Mathematical Society
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1090/tran/6953

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