JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HOW THE PARAMETER ε INFLUENCE THE GROWTH RATES OF THE PARTIAL QUOTIENTS IN GCFε EXPANSIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HOW THE PARAMETER ε INFLUENCE THE GROWTH RATES OF THE PARTIAL QUOTIENTS IN GCFε EXPANSIONS
Zhong, Ting; Shen, Luming;
  PDF(new window)
 Abstract
For generalized continued fraction (GCF) with parameter , we consider the size of the set whose partial quotients increase rapidly, namely the set $$E_{\epsilon}({\alpha}):
 Keywords
expansion;Engel series expansion;parameter function;growth rates;Hausdorff dimension;
 Language
English
 Cited by
1.
Some dimension relations of the Hirst sets in regular and generalized continued fractions, Journal of Number Theory, 2016, 167, 128  crossref(new windwow)
 References
1.
K. J. Falconer, Fractal Geometry, Mathematical Foundations and Application, Wiley, 1990.

2.
F. Schweiger, Continued fraction with increasing digits, Oster Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 212 (2003), 69-77.

3.
L. M. Shen and Y. Zhou, Some metric properties on the GCF fraction expansion, J. Number Theory 130 (2010), no. 1, 1-9. crossref(new window)

4.
J. Wu, How many points have the same Engel and Sylvester expansions, J. Number Theory 103 (2003), no. 1, 16-26. crossref(new window)

5.
T. Zhong, Metrical properties for a class of continued fractions with increasing digits, J. Number Theory 128 (2008), no. 6, 1506-1515. crossref(new window)

6.
T. Zhong and L. Tang, The growth rate of the partial quotients in a class of continued fractions with parameters, J. Number Theory 145 (2014), 388-401. crossref(new window)