Explicit continued fractions with expected partial quotient growth
HTML articles powered by AMS MathViewer
- by Takeshi Okano PDF
- Proc. Amer. Math. Soc. 130 (2002), 1603-1605 Request permission
Abstract:
For $0<x<1$ let $[0,a_1(x),a_2(x),\dots ]$ be the continued fraction expansion of $x$. Write \[ L_N(x)=\max _{1\le n\le N}a_n(x).\] We construct some numbers $x$’s with \[ \lim _{N\to \infty }\inf N^{-1}L_N(x)\log \log N=1/\log 2.\]References
- Walter Philipp, A conjecture of Erdős on continued fractions, Acta Arith. 28 (1975/76), no. 4, 379–386. MR 387226, DOI 10.4064/aa-28-4-379-386
Additional Information
- Takeshi Okano
- Affiliation: Department of Mathematics, Saitama Institute of Technology, Okabe-machi, Saitama 369-0293, Japan
- Email: okano@sit.ac.jp
- Received by editor(s): January 2, 2001
- Published electronically: January 21, 2002
- Communicated by: David E. Rohrlich
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1603-1605
- MSC (2000): Primary 11A55; Secondary 11K50
- DOI: https://doi.org/10.1090/S0002-9939-02-06337-2
- MathSciNet review: 1887004