Transference inequalities for multiplicative Diophantine exponents

2010/12/09 by Oleg N. German, German, Oleg N.
Mathematics · #11H46 #11H60 #11J25 #11J82 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1012.2071

openalex publication_date 2010/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove inequalities for multiplicative analogues of Diophantine exponents, similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if and only if its transpose is badly approximable and establish some inequalities connecting multiplicative exponents with ordinary ones.

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