On factorization of entire functions satisfying differential equations (Q1175419)

A function \(f\) meromorphic in the plane is called pseudo-prime if any factorization \(h=f\circ g\) into meromorphic functions \(f\) and \(g\) yields that either \(f\) or else \(g\) is a rational function. In this paper various criteria for pseudo-primeness are proved, referring to solutions of differential equations. We quote one result on certain solutions of a nonlinear algebraic differential equation of the second order: (*) \(P(z,w,w',w'')=0\). Theorem 4: Suppose \(h\) is an entire and periodic solution of (*) satisfying \(\log\log T(r,h)=O(\log r)\) as \(r\to\infty\). Then \(h\) is pseudo-prime.