Simultaneous diophantine approximation for a restricted class of pairs of real numbers

2022/02/03 by Youssef Lazar, Lazar, Youssef
Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2202.01596

openalex publication_date 2022/02/03 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We prove that the Littlewood conjecture is satisfied for a restricted class of pairs (α,β) of badly approximable numbers. We use the localization of the roots of a cubic equation with coefficients depending on the diophantine properties for the considered pair (α,β). The estimates of the roots rely on the properties of the denominators of the convergents of the continued fraction expansion of α and β.

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