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HOW THE PARAMETER ε INFLUENCE THE GROWTH RATES OF THE PARTIAL QUOTIENTS IN GCFε EXPANSIONS
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 Title & Authors
HOW THE PARAMETER ε INFLUENCE THE GROWTH RATES OF THE PARTIAL QUOTIENTS IN GCFε EXPANSIONS
Zhong, Ting; Shen, Luming;
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 Abstract
For generalized continued fraction (GCF) with parameter , we consider the size of the set whose partial quotients increase rapidly, namely the set , where > 1. We in [6] have obtained the Hausdorff dimension of when is constant or for any . As its supplement, now we show that: . So the bigger the parameter function is, the larger the size of becomes.
 Keywords
expansion;Engel series expansion;parameter function;growth rates;Hausdorff dimension;
 Language
English
 Cited by
1.
How the dimension of some GCFϵ sets change with proper choice of the parameter function ϵ(k), Journal of Number Theory, 2017, 174, 1  crossref(new windwow)
2.
Some dimension relations of the Hirst sets in regular and generalized continued fractions, Journal of Number Theory, 2016, 167, 128  crossref(new windwow)
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J. Wu, How many points have the same Engel and Sylvester expansions, J. Number Theory 103 (2003), no. 1, 16-26. crossref(new window)

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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)

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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)