Gorodnik, Alexander; Vishe, Pankaj (2018). Diophantine approximation for products of linear maps — logarithmic improvements. Transactions of the American Mathematical Society, 370(1):487-507.
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.
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: | 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 Nov 2023 08:16 |
| 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 |
Gorodnik, Alexander