A note on Hayman’s problem and the sharing value

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Yuntong Li¹ 

[1] Department of Basic Courses, Shaanxi Railway Institute

关键词: Meromorphic functions;    uniqueness theorems;    shared value.;   

DOI  :  10.3792/pjaa.90.119

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

Let $f$ be a nonconstant meromorphic functions, $n, k$ be two positive integers. Suppose that $f^{n}$ and $(f^{n})^{(k)}$ share the value $a( \ne 0,\infty )$ CM. If either (1) $n>k+2$, or (2) $n>k+1$ and $\bar{N}(r,f)=\lambda T(r,f)(\lambda \in [0,\frac{1}{2}))$, then $f^{n}=(f^{n})^{(k)}$ and $f$ assumes the form \begin{equation*} f(\mathrm{z}) = \mathrm{ce}^{\frac{λ}{n}z} \end{equation*} where $c$ is a nonzero constant and ${\lambda}^{k}=1$.

【 授权许可】

Unknown