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Uniqueness of meromorphic functions and a question of C.C.Yang. (English) Zbl 0701.30025
The author proves the following Theorem: Let f and g be two nonconstant meromorphic functions in the plane, n be a nonnegative integer. Assume that $$f=0\rightleftarrows g=0$$, $$f=\infty \rightleftarrows g=\infty$$, $$f^{(n)}=1\rightleftarrows g^{(n)}=1$$ and $\limsup_{r\to \infty}\frac{2N(r,1/f)+(n+z)\bar N(r,f)}{T(r,f)}<1.$ Then $$f\equiv g$$ or $$f^{(n)}g(n)\equiv 1$$.
Reviewer: Fred Gross

##### MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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