## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 47, Number 3 (2017), 905-926.

### Nevanlinna uniqueness of linear difference polynomials

Nan Li, Risto Korhonen, and Lianzhong Yang

#### Abstract

In this paper, we investigate shared value problems related to an entire function $f(z)$ of hyper-order less than one and its linear difference polynomial $L(f)=\sum _{i=1}^{k}a_{i}f(z+c_{i})$, where $a_{i}, c_{i}\in \mathbb {C}$. We give sufficient conditions in terms of weighted value sharing and truncated deficiencies, which imply that $L(f)\equiv f$.

#### Article information

**Source**

Rocky Mountain J. Math., Volume 47, Number 3 (2017), 905-926.

**Dates**

First available in Project Euclid: 24 June 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1498269816

**Digital Object Identifier**

doi:10.1216/RMJ-2017-47-3-905

**Mathematical Reviews number (MathSciNet)**

MR3682154

**Zentralblatt MATH identifier**

1372.30020

**Subjects**

Primary: 30D35: Distribution of values, Nevanlinna theory 39A05: General theory

**Keywords**

Linear difference operator shared value entire function hyper-order

#### Citation

Li, Nan; Korhonen, Risto; Yang, Lianzhong. Nevanlinna uniqueness of linear difference polynomials. Rocky Mountain J. Math. 47 (2017), no. 3, 905--926. doi:10.1216/RMJ-2017-47-3-905. https://projecteuclid.org/euclid.rmjm/1498269816