The Periodicity of Entire Functions with Finite Order

Abstract

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 Qf 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 fzΔcnfz is a periodic function, then f is also a periodic function. These results extend Yang’s conjecture.