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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Explicit continued fractions with expected partial quotient growth


Author: Takeshi Okano
Journal: Proc. Amer. Math. Soc. 130 (2002), 1603-1605
MSC (2000): Primary 11A55; Secondary 11K50
Published electronically: January 21, 2002
MathSciNet review: 1887004
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Abstract: For $0<x<1$ let $[0,a_1(x),a_2(x),\dots]$ be the continued fraction expansion of $x$. Write

\begin{displaymath}L_N(x)=\max_{1\le n\le N}a_n(x).\end{displaymath}

We construct some numbers $x$'s with

\begin{displaymath}\lim_{N\to\infty}\inf N^{-1}L_N(x)\log\log N=1/\log 2.\end{displaymath}


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Additional Information

Takeshi Okano
Affiliation: Department of Mathematics, Saitama Institute of Technology, Okabe-machi, Saitama 369-0293, Japan
Email: okano@sit.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06337-2
PII: S 0002-9939(02)06337-2
Keywords: Continued fractions, measure theory
Received by editor(s): January 2, 2001
Published electronically: January 21, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society