Cubic approximation to Sturmian continued fractions

JOURNAL OF NUMBER THEORY

卷:184

Article

Schleischitz, Johannes¹ 

[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

关键词: Geometry of numbers;    Continued fractions;    Sturmian words;   

DOI  :  10.1016/j.jnt.2017.08.022

来源: Elsevier

【 摘 要 】

We determine the classical exponents of approximation w(3) (zeta), w*3(zeta), lambda 3 (zeta) and (w) over cap3 (zeta), (lambda) over cap3 (zeta) associated to real numbers zeta whose continued fraction expansions are given by a Sturmian word. We more generally provide a description of the combined graph of the parametric successive minima functions defined by Schmidt and Summerer in dimension three for such Sturmian continued fractions. This both complements similar results due to Bugeaud and Laurent concerning the two-dimensional exponents and generalizes a recent result of the author. As a side result we obtain new information on the spectra of the above exponents. Moreover, we provide some information on the exponents lambda(n) (zeta) for a Sturmian continued fraction (zeta) and arbitrary n. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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