Iteration and the Zeros of the Second Derivative of a Meromorphic Function

Abstract

Suppose that f = (f1/f2)ep where the fi are real entire functions of order less than n with only finitely many non-real zeros and P is a real polynomial of degree n. Suppose that f1, or f2 is a polynomial. It is shown that fn has at least n − 2 distinct non-real zeros. The proof is based on the iteration of transcendental meromorphic functions.