We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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.


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
Download PDF
Publisher Web site:
Publisher statement:© 2016 American Mathematical Society. First published in Transactions of the American Mathematical Society in (April 2016), published by the American Mathematical Society.
Date accepted:16 April 2016
Date deposited:28 April 2016
Date of first online publication:16 April 2016
Date first made open access:28 April 2016

Save or Share this output

Look up in GoogleScholar