A measure estimate in geometry of numbers and improvements to Dirichlet's theorem

2021/08/10 by Kleinbock, Dmitry, Strömbergsson, Andreas, Yu, Shucheng · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2108.04638

Abstract

Let ψ be a continuous decreasing function defined on all large positive real numbers. We say that a real m× n matrix A is ψ-Dirichlet if for every sufficiently large real number t one can find \boldsymbolp ∈ ℤ^m, \boldsymbolq ∈ ℤⁿ\smallsetminus\\boldsymbol0\ satisfying ‖A\boldsymbolq-\boldsymbolp‖^m< ψ(t) and ‖\boldsymbolq‖ⁿ

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