Abstract
In this paper, we mainly study the uniqueness of specific q-shift difference polynomials and of meromorphic functions, which share a common small function and get the corresponding results. In addition, we also investigate the problem of value distribution on q-shift difference polynomials of entire functions.
Highlights
In recent years, many Scholars have been interested in value distribution of difference operators of meromorphic functions
We investigate the problem of value distribution on q-shift difference polynomials of entire functions
Many Scholars have been interested in value distribution of difference operators of meromorphic functions
Summary
Many Scholars have been interested in value distribution of difference operators of meromorphic functions (see [1]-[6]). Our purpose in the paper is to study the value distribution for q-shift polynomials of transcendental meromorphic with zero order, and some results about entire functions. Liu et al [14] have considered and proved the uniqueness of q-shift difference polynomials of meromorphic functions. Liu et al [14] considered some properties of q-shift difference polynomials of entire functions, as follow: Theorem C. Let f ( z) and g ( z) be two transcendental entire functions with ρ= ( f ) ρ= ( g ) 0 , and let α ( z) be a common small function of f ( z) and g ( z) , and let k be the number of distinct zeros of Pn ( z). ( ) ( ) Pn w1 d w1 qjz +cj v j − Pn w2 d w2 qjz +cj vj
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