Metrical properties for a class of continued fractions with increasing digits
Metrical properties for a class of continued fractions with increasing digits
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DOI：
10.1016/j.jnt.2007.03.014
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发表时间：
2008-06
影响因子：
0.7
通讯作者：
T. Zhong
中科院分区：
文献类型：
--
作者：
T. Zhong
2002年，Hartono， Kraaikamp和Schweiger引入了Engel连分式（ECF），其部分商是递增的。后来，Schweiger将其推广为一类具有递增数字和参数ε的连分数，称为广义连分数（GCF）。在本文中，我们将给出这种展开式的一些算术性质，并证明GCF在−1< ε≤1的条件下与ECF具有相似的度量性质。但当ε = - 1时，就不是这样了。
In 2002, Hartono, Kraaikamp and Schweiger introduced the Engel continued fractions (ECF), whose partial quotients are increasing. Later, Schweiger generalized it into a class of continued fractions with increasing digits and a parameter ϵ, called generalized continued fractions (GCF). In this paper, we will give some arithmetic properties of such an expansion, and show that the GCF holds similar metric properties with ECF under the condition that −1<ϵ⩽1. But when it comes to the condition that ϵ=−1, it does not.