## Taiwanese Journal of Mathematics

### 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.

#### Article information

Source
Taiwanese J. Math., Volume 18, Number 3 (2014), 701-709.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706435

Digital Object Identifier
doi:10.11650/tjm.18.2014.3802

Mathematical Reviews number (MathSciNet)
MR3213381

Zentralblatt MATH identifier
1357.30024

#### Citation

Zhang, Jie; Zhang, Jianjun; Liao, Liangwen. ENTIRE FUNCTIONS SHARING ZERO CM WITH THEIR HIGH ORDER DIFFERENCE OPERATORS. Taiwanese J. Math. 18 (2014), no. 3, 701--709. doi:10.11650/tjm.18.2014.3802. https://projecteuclid.org/euclid.twjm/1499706435

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