亚纯函数与其差分的唯一性

研究了亚纯函数与其差分算子分担多项式的唯一性问题,证明了:设f是一个有穷级非常数亚纯函数,p(z)(■0)是一个多项式.如果f,△_cf与△_c~2f CM分担∞,p(z),则f≡△_cf或f(z)=e~(Az+B)+b,其中p(z)≡b≠0,A≠0满足e~(Ac)=1.本文结果是对Chang, Fang(Chang J M, Fang M L. Uniqueness of entire functions and fixed points J]. Kodai Math J, 2002, 25(1):309-320.)结果的差分模拟,并且完整回答了Chen, Chen(Chen B Q, Chen Z X, Li S. Uniqueness theorems on entire functions and their difference operators or shifts J]. Abstr Appl Anal, 2012,Art. ID 906893, 8 pp.)的问题.

Unicity of Meromorphic Functions and Their Difference Operators

This paper deals with the unicity of meromorphic functions and their difference operators and proves: Let $f$ be a nonconstant meromorphic function of finite order, and let $p(z)(\not\equiv 0)$ be a polynomial. If $f, \Delta_cf$ and $\Delta_{c}^{2}f$ share $\infty$ and $ p(z)$ CM, then either $f\equiv\Delta_cf$ or $f(z)=\rme^{Az+B}+b$, where $p(z)\equiv b\neq 0$, $A\neq 0$ satisfying $\rme^{Ac}=1$. Our result provides a difference analogue of a result of Chang and Fang (Chang J M, Fang M L. Uniqueness of entire functions and fixed points J]. {\it Kodai Math J}, 2002, 25(1): 309--320.), and answers the question of Chen and Chen (Chen B Q, Chen Z X, Li S. Uniqueness theorems on entire functions and their difference operators or shifts J]. {\it Abstr Appl Anal}, 2012, Art ID 906893, 8 pp.).