Investigations on Uniqueness of Entire and Meromorphic Functions: Exploring Value Distribution and Differential Polynomials in Complex Analysis

The book “Investigation on Uniqueness of Entire and Meromorphic Functions and Their Differential Polynomials” offers a comprehensive study of uniqueness problems in complex analysis through Nevanlinna’s value distribution theory. It investigates the conditions under which two entire or meromorphic functions, or their differential polynomials, coincide when they share the same values or small functions. The work extends several classical theorems, presenting new results that reveal the intricate relationship between value sharing, growth, and order of complex functions. It also examines how derivatives and differential operations influence the uniqueness properties and behavior of these functions. Combining rigorous proofs with conceptual discussions, the book provides both theoretical depth and clarity. Its findings contribute to the ongoing development of uniqueness theory and enhance the understanding of complex differential polynomials. This volume will be a valuable resource for postgraduate students and researchers in complex analysis, particularly those exploring Nevanlinna theory, uniqueness problems, and the dynamics of entire and meromorphic functions.