Metric properties and exceptional sets of beta-continued fractions of Laurent series

2013 ◽  
Vol 83 (1-2) ◽  
pp. 1-19 ◽  
Author(s):  
MEI-YING LU
Keyword(s):  
Continued Fractions ◽  
Laurent Series ◽  
Metric Properties ◽  
Exceptional Sets

scholarly journals Metrical properties for continued fractions of formal Laurent series

2021 ◽  
Vol 73 ◽  
pp. 101850
Author(s):  
Hui Hu ◽  
Mumtaz Hussain ◽  
Yueli Yu
Keyword(s):  
Continued Fractions ◽  
Laurent Series ◽  
Formal Laurent Series

Metrical property for GCFϵ expansion with the parameter function ϵ(k) = c(k + 1)

2015 ◽  
Vol 11 (07) ◽  
pp. 2065-2072 ◽  
Author(s):  
Ting Zhong ◽  
Quanwu Mu ◽  
Luming Shen
Keyword(s):  
Continued Fractions ◽  
Partial Quotient ◽  
The Real ◽  
Metric Properties ◽  
Metrical Property ◽  
Parameter Function ◽  
Generalized Continued Fractions

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 Theory128 (2008) 1506–1515] obtained the following metrical properties: [Formula: see text] 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: [Formula: see text] which change with the real c ∈ (0, ∞). Note that [Formula: see text] as c → 0, it indicates that when c → 0, the GCFϵ has the same metrical property as the case of -1 < ϵ(kn) ≤ 1.

scholarly journals Exceptional sets of the Oppenheim expansions over the field of formal Laurent series

2016 ◽  
Vol 42 ◽  
pp. 253-268
Author(s):  
Mei-Ying Lü ◽  
Jia Liu ◽  
Zhen-Liang Zhang
Keyword(s):  
Laurent Series ◽  
Formal Laurent Series ◽  
Exceptional Sets

Metric properties of the product of consecutive partial quotients in continued fractions

2020 ◽  
Vol 238 (2) ◽  
pp. 901-943 ◽  
Author(s):  
Lingling Huang ◽  
Jun Wu ◽  
Jian Xu
Keyword(s):  
Continued Fractions ◽  
Metric Properties ◽  
Partial Quotients

Independence of continued fractions in the field of Laurent series

2007 ◽  
Vol 55 (1) ◽  
pp. 35-59
Author(s):  
Tuangrat Chaichana ◽  
Vichian Laohakosol
Keyword(s):  
Continued Fractions ◽  
Laurent Series
Sign in / Sign up

Export Citation Format

Share Document