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Proof of a conjecture of Gross concerning fix-points. (English) Zbl 0681.30014
It is proved that if f and g are transcendental entire functions and if Q is a non-constant polynomial, then the equation f(g(z))=Q(z) has infinitely many solutions. In particular, f(g(z)) has an infinite number of fix-points. This confirms a conjecture of F. Gross [Factorization of meromorphic functions (1972; Zbl 0266.30006)].
Reviewer: W.Bergweiler

MSC:
30D05Functional equations in the complex domain, iteration and composition of analytic functions
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