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Explicit continued fractions with expected partial quotient growth

Author(s): Takeshi Okano
Journal: Proc. Amer. Math. Soc. 130 (2002), 1603-1605.
MSC (2000): Primary 11A55; Secondary 11K50
Posted: January 21, 2002
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Abstract | References | Similar articles | Additional information

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

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

References:

1.: W. Philipp, A conjecture of Erdös on continued fractions, Acta. Arith. 28 (1976), 379-386. MR 52:8069


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