On certain criteria for the primality of meromorphic functions (Q807768)

The authors prove a number of interesting results on the primality of meromorphic functions. Among other things they prove the following: Let \(f\) be a transcendental meromorphic function, then there exists an integer \(n\) such that the set \(\{a\in \mathbb C; f(z)z^ n(z-a)\) is not prime \(\}\) is an at most countable set. This partially resolves a problem posed by the reviewer together with Osgood and Yang, namely: Given any transcendental meromorphic function \(f\), does there exist an entire function \(g\) such that \(f\circ g\) is prime?