Further results on prime entire functions

Fred Gross, Chung Chun Yang
1974 Transactions of the American Mathematical Society  
Let H denote the set of all the entire functions f(z) of the form: f(z) = h(z)eM + k(z) where p(z) is a nonconstant polynomial of degree m, and A(# 0), k (# constant) are two entire functions of order less than m. In this paper, a necessary and sufficient condition for a function in H to be a prime is established. Several generalizations of known results follow. Some sufficient conditions for primeness of various subclasses of H are derived. The methods used in the proofs are based on
more » ... 's theory of meromorphic functions and some elementary facts about algebraic functions.
doi:10.1090/s0002-9947-1974-0349972-3 fatcat:qxs5uggnpnhyjah4xgtfyrroxq