亚纯函数的导函数分担集合的唯一性

Set Sharing Results for Derivatives of Meromorphic Functions

中文关键词:  亚纯函数  分担集合  唯一性定理

英文关键词:meromorphic function  shared set  uniqueness theorem

中文摘要:

      研究了两个亚纯函数的导函数分担两个值集的唯一性问题. 证明了对于集合$S$和$T$, 如果$\overline{E}_{f^{(k)}}(S)=\overline{E}_{g^{(k)}}(T)$, 则存在非零常数$A$, 使得$f^{(k)}=Ag^{{(k)}}$. 特别地, 当$k=0$时, 有$f=Ag$.

英文摘要:

      In this paper, we investigate the uniqueness of the derivatives of meromorphic functions sharing two different sets, and obtain the result that if two transcendental meromorphic functions $f$ and $g$ satisfy $\overline{E}_{f^{(k)}}(S)=\overline{E}_{g^{(k)}}(T)$, then $f^{(k)}=Ag^{(k)}$, where $S$, $T$ are two finite sets and $A$ is a nonzero constant. In particular, $k=0$ implies $f=Ag$.