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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
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