During the years the investigation of the characteristic function of differential-difference polynomials is a long-cherished phenomenon and the results obtained in this direction can be viewed as a differential-difference analogue of the classical Valiron-Mokhon'ko Theorem (Year)and in this connection, it is necessary to investigate the deficiencies of some homogeneous differential-difference polynomials. Some characteristics of special differential-difference polynomials are also investigated and subsequent results on this topic can be estimated as differential-difference analogues of some...

Classical value distribution theory deals with the study of the density of points in the plane at which an analytic function takes a prescribed value. Polynomials for which complete results can at once be obtained, served as a model when the study of entire functions was started about a hundred years ago. In 1926 Finish mathematician Rolf Nevanlinna succeeded in creating a far-reaching value distribution theory for meromorphic functions in such a way that it can be mentioned as a special case of the theory of entire functions in an improved form. Recently p-adic Nevanlinna theory has become...

In the twentieth century, the theory of value distribution for meromorphic functions of one complex variable has already been developed in the field of complex analysis. Although it has a long history, there are still some interesting and remarkable results in the recent years. Knowledge of the behavior of logarithmic derivative of an entire function has become useful in the study of many problems in value distribution theory.In this monograph we consider the behavior of integrated moduli of logarithmic derivative as it relates to the Nevanlinna's characteristic of a function. Renowned...