## Normality and shared values concerning differential polynomials.(English)Zbl 1213.30055

Let $${\mathcal F}$$ be a family of meromorphic functions in a domain $$D$$, and let $$P$$ be a polynomial with either $$\deg P \geq 3$$ or $$\deg P=2$$, and $$P$$ having only one zero. In this paper, the authors prove that if there is a non-zero complex number $$b$$ such that, for any $$f \in {\mathcal F}$$ and $$g \in {\mathcal F}$$, $$P(f)f'$$ and $$P(g)g'$$ share $$b$$ in $$D$$, then $${\mathcal F}$$ is normal in $$D$$. The authors also give two examples showing that the theorem fails when $$\deg P=1$$ or $$b=0$$.
Reviewer: Zhuan Ye (DeKalb)

### MSC:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D45 Normal functions of one complex variable, normal families

### Keywords:

meromorphic function; normal family; shared value
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### References:

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