Diophantine approximation for products of linear maps -- logarithmic improvements

Alexander Gorodnik, Pankaj Vishe

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
289 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)487-507
Number of pages21
JournalTransactions of the American Mathematical Society
Issue number1
Early online date21 Jun 2017
Publication statusPublished - 1 Jan 2018


  • math.NT
  • math.DS


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