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Department of Mathematical Sciences


Publication details for Pankaj Vishe

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

Author(s) from Durham


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.