## Meromorphic functions that share three sets.(English)Zbl 0882.30019

Let $$n$$ be a positive integer, and let $$w= \exp (2\pi i/n)$$. Let $$S_1= \{1,w,w^2, \dots, w^{n-1}\}$$, $$S_2 =\{0\}$$, and $$S_3= \{\infty\}$$. The author proves six theorems which are improvements or supplements to known results. A typical theorem assumes $$f$$ and $$g$$ are nonconstant meromorphic functions in the plane which share sets $$S_1$$ and $$S_3$$, counting multiplicity, and $$S_2$$ ignoring multiplicity and proves that if $$n\geq 2$$, then $$f=tg$$ where $$t^n=1$$ or $$f\cdot g=s$$ where $$s^n=1$$.
Reviewer: L.R.Sons (DeKalb)

### MSC:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D30 Meromorphic functions of one complex variable (general theory) 30D20 Entire functions of one complex variable (general theory)
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### References:

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