Diophantine approximation for products of linear maps -- logarithmic improvements

Alexander Gorodnik; Pankaj Vishe

doi:10.1090/tran/6953

Diophantine approximation for products of linear maps -- logarithmic improvements

Alexander Gorodnik, Pankaj Vishe

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Pages (from-to)	487-507
Number of pages	21
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	1
Early online date	21 Jun 2017
DOIs	https://doi.org/10.1090/tran/6953
Publication status	Published - 1 Jan 2018

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math.NT
math.DS

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10.1090/tran/6953

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Diophantine approximation for products of linear maps -- logarithmic improvements

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