涉及亚纯函数差分算子的唯一性定理
Uniqueness of Meromorphic Function Concerning Difference Operator

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)) < 1的亚纯函数。令η是满足Δ_ηf(z)？0的非零常数。如果f(z)和Δ_ηf(z)CM分担Δ_ηa(z),b(z)，那么，a(z)=0，b(z)=∞，f(z)=Be^Az，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。
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)) < 1. Let η be a nonzero constant satisfying Δ_ηf(z)？0. If f(z) and Δ_ηf(z) share Δ_ηa(z),b(z) CM, then a(z)=0，b(z)=∞，f(z)=Be^Az, where A,B are non-zero constants. Our result is an improvement of the theorem given by Chen and Zhang.