Constructing Simultaneous Diophantine Approximations of Certain Cubic Numbers

2014/12/12 by Dustin Hinkel, Hinkel, Dustin
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Advanced Mathematical Theories and Applications #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1412.3936

Abstract

For K a cubic field with only one real embedding and α,β∈ K, we show how to construct an increasing sequence \m_n\ of positive integers and a subsequence \ψ_n\ such that (for some constructible constants C₁,C₂>0) max\‖m_nα‖,‖m_nβ‖\

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