与高阶导数分担多项式的整函数

基金项目:

国家自然科学基金

详细信息

Entire Functions Sharing Polynomial With Their Higher Order Derivative

摘要: 证明了如果 $~f~$ 是非常数整函数满足超级 $~\sigma_{2}(f)<\frac{1}{2}~$ ,~ $~k~$ 是一正整数,~如果 $~f~$ 和 $~f^{(k)}~$ 分担多项式 $~p(z)~$ ~CM,~其中 $~p(z)=a_{m}z^{m}+a_{m-1}z^{m-1}+\cdots+a_{0}~$ ~( $~a_{m}\neq 0,~a_{m-1},~\ldots,~a_{0}~$ 均为常数)~,~那么 $~f^{(k)}(z)-p(z)=c(f(z)-p(z))~$ ,~其中 $~c~$ 是非零常数.
- 超级
Abstract: It is shown that if $f$ be a nonconstant entire function such that the hyper order $\sigma_{2}(f)<\frac{1}{2}$ ,~ $k$ being a positive integer,~and if $f$ and $f^{(k)}$ share polynomial $p(z)$ CM,~where $p(z)=a_{m}z^{m}+a_{m-1}z^{m-1}+\cdots+a_{0}$ with $a_{m}\neq 0,~a_{m-1},~\ldots,~a_{0}$ are all constants,~then $f^{(k)}(z)-p(z)=c(f(z)-p(z))$ where $c$ is a nonzero constant.
- Hyper-order