Nevanlinna theory and its applications

This thesis consist of three chapters. In first chapter, we give definitions and theorems which compose a basic for next chapters. In second chapter, the second part is introduction an introduction to the Nevanlinna theory. A positive logarithm definition is given and the inequalities associated with it are proved. Notations of the zero and pole points of the meromorphic functions are given, and the characteristics of the meromorphic functions are described by using these notations. The first and second principal theorems that form the basis for the Nevanlinna Theorem have been proved and the meaning of f(z)=O(1) has been given. The order and type definitions of entire and meromorph functions are indicated and classified. Finally, Nevanlinna's second basic theorem is proved. In the third chapter, a characteristic integral is developed for the functions increasing with the finite logarithmic order. Subsequently, some properties of f a meromorphic function and the characteristic expression T(r,f) of the function are given, and the approximate logarithmic order and convergence logarithmic exponent definitions are denoted. In the continuation of this section, we are interested in the finite double-logarithmic order.