Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11A55, 11K50

Retrieve articles in all journals with MSC (2000): 11A55, 11K50

Additional Information

Takeshi Okano
Affiliation: Department of Mathematics, Saitama Institute of Technology, Okabe-machi, Saitama 369-0293, Japan

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia