On Factorization of Certain Entire-Functions

Let P and Q be polynomials and let α be an entire function. Suppose that Q and α are nonconstant. We show that the function h(z) = P(z)eα(z) + Q(z) has a factorization h(z) = ƒ(g(z)) with nonlinear meromorphic left and right factors ƒ and g if and only if P, Q, and α have such a factorization with a common right factor. This confirms conjectures of F. Gross, G. D. Song, and C. C. Yang.