ENTIRE FUNCTIONS SHARING ZERO CM WITH THEIR HIGH ORDER DIFFERENCE OPERATORS

Abstract

In this paper, we investigate uniqueness of entire functions of order less than 2 sharing the value 0 with their difference operators and obtain a result as follows: Let $f$ be a transcendental entire function such that $\sigma{(f)}\lt 2$ and $\lambda(f)\lt \sigma{(f)}$. If $f$ and $\Delta^nf$ share the value $0$ CM, then $f$ must be form of $f(z)=Ae^{\alpha z},$ where $A$ and $\alpha$ are two nonzero constants. This result confirms a conjecture posed earlier on the topic.