Borel Directions and the Uniqueness of Algebroid Functions Dealing with Multiple Values

2021 ◽  
Vol 58 (1) ◽  
pp. 104-118
Author(s):  
Yang Tan ◽  
Qingcai Zhang
Keyword(s):  
Conformal Mapping ◽  
Meromorphic Functions ◽  
Angular Domain ◽  
Uniqueness Results ◽  
Algebroid Functions

In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.

scholarly journals Borel Directions and Uniqueness of Meromorphic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Keyu Zhang ◽  
HongYan Xu ◽  
Hongxun Yi
Keyword(s):  
Meromorphic Functions ◽  
Angular Domain ◽  
Recent Theorem ◽  
The Relationship

We investigate the relationship between Borel directions and uniqueness of meromorphic functions and obtain some results of meromorphic functions sharing four distinct values IM and one set in an angular domain containing a Borel line. Our result is an improvement of a recent theorem given by Long and Wu (2012).

scholarly journals An Inequality of Meromorphic Functions and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhaojun Wu ◽  
Yuxian Chen ◽  
Zuxing Xuan
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Angular Domain ◽  
Covering Surface

By applying Ahlfors theory of covering surface, we establish a fundamental inequality of meromorphic function dealing with multiple values in an angular domain. As an application, we prove the existence of some new singular directions for a meromorphic functionf, namely a Bloch direction and a pseudo-T direction forf.

scholarly journals The Unique Range Set of Meromorphic Functions in an Angular Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hong-Yan Xu ◽  
Zu-Xing Xuan ◽  
Hua Wang
Keyword(s):  
Meromorphic Functions ◽  
Angular Domain ◽  
Shared Set ◽  
Unique Range Set

By using Tsuji's characteristic, we investigate uniqueness of meromorphic functions in an angular domain dealing with the shared set, which is different from the set of the paper (Lin et al., 2006) and obtain a series of results about the unique range set of meromorphic functions in angular domain.

Sharing sets of q-difference of meromorphic functions

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Xiaoguang Qi ◽  
Lianzhong Yang
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Zero Order ◽  
Partial Answer ◽  
Uniqueness Results

AbstractThis paper is devoted to proving some uniqueness results for meromorphic functions f(z) share sets with f(qz). We give a partial answer to a question of Gross concerning a zero-order meromorphic function f(z) and its q-difference f(qz).

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