[PDF] Top 20 Uniqueness and value distribution for difference operators of meromorphic function

... The difference Nevanlinna theory and its applications to the uniqueness theory have become a subject of great interest [2-4], ...a meromorphic function f (z) sharing values with its shift f(z ... See full document

... and uniqueness of com- plex difference polynomials of meromorphic ...Nevanlinna value distribution theory of meromorphic functions are used (see [, ...a meromorphic ... See full document

... their difference operators (see, ...the uniqueness problems on the case that shifts or differ- ence polynomials of two entire functions share a small ...the uniqueness problems of ... See full document

... a meromorphic function play key roles in the construction and applications of classical Nevanlinna ...studying difference equations in the complex ...on difference operator. Bergweiler and ... See full document

... the value distribution of a meromorphic function f (z) concerning its derivative f (z) and q-shift difference f (qz + c), where f(z) is of finite logarithmic ...the uniqueness of ... See full document

... counting function of poles of f , and N(r, f ) is called the reduced counting function of poles of f ...characteristic function of f , and it plays a cardinal role in the whole theory of ... See full document

... Remark 1.9. Some results about the zeros distributions of difference polynomials of entire functions or meromorphic functions with the condition λ1/f < ρf can be found in 9– 12. Theorem 1.7 is a partial ... See full document

... of Meromorphic functions is an important part of Nevan- linna ...to difference operators. This has lead to development of difference counterparts of many central results of Nevanlinna theory ... See full document

... non-constant meromorphic function f(z), if f(z) and f(z+c) share 3 distinct non-zero, finite values( or small functions) IM, they must ...entire function f(z) the number of shared values must be 2, ... See full document

... of Meromorphic functions is an important part of Nevan- linna ...to difference operators. This has lead to development of difference counterparts of many central results of Nevanlinna theory ... See full document

... Recently, a number of papers (including [–]) have focused on difference analogues of Nevanlinna theory. In addition, many papers have been devoted to the investigation of the uniqueness problems related to ... See full document

... non-constant meromorphic functions of finite order and their difference operators are identical, if they share four small functions “IM”, or share two small functions and ∞ ...the uniqueness of a ... See full document

... the value distribution of a meromorphic function from the whole plane to an angular ...the uniqueness problem under the condition that five values and four values are shared in some ... See full document

... the uniqueness of specific q-shift difference polynomials of meromorphic functions by Nevanlinna and value distribution theory and extend previous ...of value distribution ... See full document

... Let f (z) and g(z) be two nonconstant meromorphic functions, and let a be an arbitrary complex constant. If f (z) – a and g(z) – a have the same zeros counting multiplicities (ig- noring multiplicities), we say ... See full document

... of Meromorphic functions is an important part of Nevan- linna ...difference operators. Then many authors started to investigate the uniqueness of meromorphic functions sharing values ... See full document

... the value distribution theory [4]. For any nonconstant meromorphic function f (z) on the complex plane C, we denote by S(r, f ) any quantity satisfying S(r, f ) = o(T(r, f )) as r → ∞ except ... See full document

... nonconstant meromorphic functions f and g , by N(r, a; f | g = b) (N(r, a; f | g = b)) we mean the counting function of those a-points of f that are (not) the b-points of g, where an a-point of f is counted ... See full document

... the value distribution of difference polynomial and obtain the following result, which improves a recent result of ...transcendental meromorphic function of finite order σ , c be a nonzero ... See full document

... We use Nevanlinna’s value distribution theory of meromorphic functions (see [1, 2]) as the main tool in the whole paper. In what follows, the growth order of w(z) is represented by σ (w) and the ... See full document