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Periodica Mathematica Hungarica

, Volume 66, Issue 1, pp 95–103 | Cite as

Optimal continued fractions and the moving average ergodic theorem

  • H. Kamarul Haili
  • R. Nair
Article

Abstract

We use the moving average ergodic theorem of A. Bellow, R. Jones and J. Rosenblatt to derive various results in metric number theory primarily concerning moving averages of various sequences attached to the optimal continued fraction expansion of a real number.

Key words and phrases

optimal continued fractions moving averages ergodic theorems 

Mathematics subject classification numbers

11K50 28D99 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversiti Sains Malaysia, MindenPenangMalaysia
  2. 2.Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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