On factorization of meromorphic functions with finitely many poles (Q2724885)

Let \(F\) be a meromorphic function. \(F\) is said pseudo-prime if every factorization of \(F\) in the form \(F=f(g(z))\) with \(f\) meromorphic and \(g\) entire implies that either \(f\) is rational or \(g\) is a polynomial. If \(F\) is of infinite order, there is no criteria for determining the pseudo-primeness. In this paper, the authors give some criteria for the pseudo-primeness, connected to the localization and dispersion of the zeros and poles of \(F\), which hold also for functions of infinite order.