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Archiv der Mathematik

, Volume 112, Issue 2, pp 161–168 | Cite as

Über die Funktionen des Irrationalitätsmaßes für zwei irrationale Zahlen

  • Nikolay MoshchevitinEmail author
Article
  • 13 Downloads

Abstract

For real \(\xi \) we consider the irrationality measure function \(\psi _\xi (t) = \min _{1\leqslant q \leqslant t, \, q\in \mathbb {Z}} ||q\xi ||\). We prove that in the case \(\alpha \pm \beta \not \in \mathbb {Z}\) there exist arbitrary large values of t with \(|\psi _\alpha (t) -\psi _\beta (t)| \geqslant \left( \sqrt{\frac{\sqrt{5}+1}{2}}-1\right) \min (\psi _\alpha (t), \psi _\beta (t))\). This result is optimal.

Keywords

Irrationality measure function Continued fractions 

Mathematics Subject Classification

11J70 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Steklow-Institut für Mathematik der Russischen Akademie der WissenschaftenGubkina 8, MoskauRussia

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