Metrical property for GCFϵ expansion with the parameter function ϵ(k) = c(k + 1)
Metrical property for GCFϵ expansion with the parameter function ϵ(k) = c(k + 1)
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DOI：
10.1142/s179304211550089x
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发表时间：
2015-10
影响因子：
0.7
通讯作者：
T. Zhong;Q. Mu;Luming Shen
中科院分区：
文献类型：
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作者：
T. Zhong;Q. Mu;Luming Shen
本文讨论了参数函数为ε (kn)的广义连分数（gcf御）的度量性质，其中kn是gcf御展开的n次偏商。当-1 < λ (kn)≤1时，Zhong[一类递增数连分数的格律性质，J.数论128(2008)1506-1515]得到了以下格律性质：这与选择λ (kn)∈(- 1,1)完全无关。这里我们处理的情况是，当常数c∈(0,∞)时，λ (k) = c（k + 1）。证明了：随实数c∈(0,∞)变化。注意，当c→0时，表明当c→0时，gcf御柱与-1 <御柱(kn)≤1时具有相同的测量性质。
This paper is concerned with the metric properties of the generalized continued fractions (GCFϵ) with the parameter function ϵ(kn), where kn is the nth partial quotient of the GCFϵ expansion. When -1 < ϵ(kn) ≤ 1, Zhong [Metrical properties for a class of continued fractions with increasing digits, J. Number Theory 128 (2008) 1506–1515] obtained the following metrical properties: which are entirely unrelated to the choice of ϵ(kn) ∈ (-1, 1]. Here we deal with the case of ϵ(k) = c(k + 1) with constant c ∈ (0, ∞). It is proved that: which change with the real c ∈ (0, ∞). Note that as c → 0, it indicates that when c → 0, the GCFϵ has the same metrical property as the case of -1 < ϵ(kn) ≤ 1.