Value distribution of differential difference polynomials and its applications

Abstract

The study of advanced complex analysis introduces the concepts of entire and meromorphic newlinefunctions along with its zeros and singularities. In the last century, renowned newlinemathematician E. Borel introduced the notion of order of a function to study the growth newlineof transcendental entire functions. The collaborated work of C. Picard and E. Borel, the newlinerenowned Picard-Borel theorem, laid the foundation for the theory of value distribution. newlineBesides, R. Nevanlinna introduced the concept of characteristic function to study newlinethe growth of zeros of meromorphic function which opened up many research prospective. newlineLater, the value distribution theory adapted to Nevanlinna theory was extensively used to newlinestudy the zeros and poles of many types of differential-difference polynomials of entire newlineand meromorphic functions and its extensions. In this thesis, the focus is to study the applicability newlineof Nevanlinna theory to some of the major research problems and extend them newlineto differential-difference category of polynomials.