Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-19T05:35:45.690Z Has data issue: false hasContentIssue false
  • English
  • Français

Appendix to the paper by T. Łuczak—A simple proof of the lower

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  26 February 2010

Fend De-Jun ,
Wu Jun ,
Jyh-Ching Liang  and
Shiojenn Tseng
Fend De-Jun
Affiliation:
Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China.
Wu Jun
Affiliation:
Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China.
Jyh-Ching Liang
Affiliation:
Department of Mathematics, Tamkang University, Tamsui, Taiwan 25137, R.O.C.
Shiojenn Tseng
Affiliation:
Department of Mathematics, Tamkang University, Tamsui, Taiwan 25137, R.O.C.
Get access

Extract

In this note we point out that a simple proof of the lower bound of the sets (b, c), and so also of Ξ(b, c), defined in the previous paper [1] can be obtained as a simple application of a general method. By Example 4.6 from [2], if [0, 1] = E0⊃E1⊃ … are sets each of which is a finite union of disjoint closed intervals such that each interval of Ek−1, contains at least mk intervals of Ek which are separated by gaps of lengths at least εk, and if mk≥2 and εk≥εk+1>0, then the dimension of the intersection of Ek is at least

MSC classification

Secondary: 11J70: Continued fractions and generalizations
Type
Research Article
Information
Mathematika , Volume 44 , Issue 1 , June 1997 , pp. 54 - 55
Copyright
Copyright © University College London 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Luczak, T.. On the fractional dimension of sets of continued fractions. Mathematika, 44 (1997), 50–53.CrossRefGoogle Scholar
2.Falconer, K.. Fractal Geometry (Wiley, 1990)Google Scholar