%0 Journal Article
%T 涉及亚纯函数差分算子的唯一性定理<br>Uniqueness of Meromorphic Function Concerning Difference Operator
%A 邱仕林
%A 郑瑞林
%A 刘丹
%J Pure Mathematics
%P 209-217
%@ 2160-7605
%D 2022
%I Hans Publishing
%R 10.12677/PM.2022.121025
%X <div style=\"text-align:justify;\">
	本文运用Nevanlinna值分布论研究了有穷级亚纯函数与其差分算子分担函数的问题，得到了如下结果。设f(z)是有穷级超越亚纯函数，a(z)(？∞),b(z)是f(z)的Borel例外函数且a(z),b(z)∈S(f)，其中a(z)是满足ρ(a(z)) &lt; 1的亚纯函数。令η是满足Δ<sub>η</sub>f(z)？0的非零常数。如果f(z)和Δ<sub>η</sub>f(z)CM分担Δ<sub>η</sub>a(z),b(z)，那么，a(z)=0，b(z)=∞，f(z)=Be<sup>Az</sup>，其中A,B是非零常数。本文是对陈创鑫和张然然结果的改进和推广。<br />
In this paper, we study the uniqueness of meromorphic functions by Nevanlinna value distribution theory and obtain the following result. Let f(z) be a transcendental meromorphic function of finite order and a(z)(∈S(f)),b(z)(∈S(f)) be a Borel exceptional function of f(z), where a(z)(？∞) is a meromorphic function satisfying ρ(a(z)) &lt; 1. Let η be a nonzero constant satisfying Δ<sub>η</sub>f(z)？0. If f(z) and Δ<sub>η</sub>f(z) share Δ<sub>η</sub>a(z),b(z) CM, then a(z)=0，b(z)=∞，f(z)=Be<sup>Az</sup>, where A,B are non-zero constants. Our result is an improvement of the theorem given by Chen and Zhang.
</div>
%K 亚纯函数，唯一性，差分算子<br>Meromorphic Function
%K Uniqueness
%K Difference Operator
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=48373