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Meromorphic functions that share fixed-points. (English) Zbl 1030.30028
Let $$f(z)$$ and $$g(z)$$ be two meromorphic functions, $$n\geq 11$$. If $$f^n(z) f'(z)- z$$ and $$g^n(z) g'(z)- z$$ assume the same zeros with the same multiplicities, then either $f(z)= c_1 e^{cz^2},\quad g(z)= c_2 e^{-cz^2}\quad (4(c_1 c_2)^{n+ 1}C^2= -1)$ or $f(z)= tg(z)\qquad (t^{n+1}= 1).$ .

##### MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D30 Meromorphic functions of one complex variable, general theory
##### Keywords:
meromorphic function; uniqueness theorem; fixed point
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##### References:
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