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October 2014 A note on Hayman’s problem and the sharing value
Yuntong Li
Proc. Japan Acad. Ser. A Math. Sci. 90(8): 119-122 (October 2014). DOI: 10.3792/pjaa.90.119

Abstract

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 ${\lambda}^{k}=1$.

Citation

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Yuntong Li. "A note on Hayman’s problem and the sharing value." Proc. Japan Acad. Ser. A Math. Sci. 90 (8) 119 - 122, October 2014. https://doi.org/10.3792/pjaa.90.119

Information

Published: October 2014
First available in Project Euclid: 3 October 2014

zbMATH: 1308.30037
MathSciNet: MR3266745
Digital Object Identifier: 10.3792/pjaa.90.119

Subjects:
Primary: 30D35

Keywords: meromorphic functions , Shared value , Uniqueness theorems

Rights: Copyright © 2014 The Japan Academy

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Vol.90 • No. 8 • October 2014
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