Electron. J. Diff. Equ., Vol. 2014 (2014), No. 233, pp. 1-10.

Value distribution of the q-difference product of entire functions

Na Xu, Ting-Bin Cao, Chun-Ping Zhong

Abstract:
For a complex value $q\neq 0, 1$, and a transcendental entire function f(z) with order $0<\sigma(f)<\infty$, we study the value distribution of q-difference product f(z)f(qz) and $f^{n}(z)(f(qz)-f(z))$. Properties of entire solution of a certain q-difference linear equation are also considered.

Submitted April 7, 2014. Published November 3, 2014.
Math Subject Classifications: 30D35, 39A05.
Key Words: Nevanlinna theory; q-difference; entire function.

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Na Xu
School of Mathematical Sciences, Xiamen University
Xiamen 361005, China
email: xuna406@163.com
Ting-Bin Cao
Department of Mathematics, Nanchang University
Nanchang, Jiangxi 330031, China
email: tbcao@ncu.edu.cn
Chun-Ping Zhong
School of Mathematical Sciences, Xiamen University
Xiamen 361005, China
email: zcp@xmu.edu.cn

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