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Explicit continued fractions with expected partial quotient growth

Authors:	Takeshi Okano

Institution:	Department of Mathematics, Saitama Institute of Technology, Okabe-machi, Saitama 369-0293, Japan

Abstract:	For let $0,a_1(x),a_2(x),\dots]$ be the continued fraction expansion of . Write $\begin{displaymath}L_N(x)=\max_{1\le n\le N}a_n(x).\end{displaymath}$ We construct some numbers 's with $\begin{displaymath}\lim_{N\to\infty}\inf N^{-1}L_N(x)\log\log N=1/\log 2.\end{displaymath}$

Keywords:	Continued fractions measure theory

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