The periodicity of entire functions with finite order (Q2036118)

Summary: This paper is concerned with the periodicity of entire functions with finite growth order, and some sufficient conditions are given. Let \(f\) is a transcendental entire function with finite growth order, zero is a Picard exceptional value of \(f\), and a given differential monomial \(Q(f)\) of \(f\) is periodic, then \(f\) is also periodic. We are also interested in finding the following: let \(f\) is a transcendental entire function with finite growth order, \(d\) is a Picard exceptional value of \(f\) and \(f(z)\Delta_c^n f(z)\) is a periodic function, then \(f\) is also a periodic function. These results extend Yang's conjecture.