Résumé:
Nevanlinna theory was created to provide a quantitative measure of the value distribution of meromorphic functions.
This theory originated over ninety years ago and still plays a very important role in the study of solutions of linar/non-linear differential equations in the complex domain.
This thesis is divided into introduction and two chapters. In the rst chapter, we shall adopt the standard notations in Nevanlinna s value distribution theory of meromorphic functions.
For example, the characteristic function T (r; f ), the counting function of the poles N (r; f ), and the proximity function m(r; f ) (see, [4],[3]).
We use (f ) to denote the order of growth of f and (f ) to denote the exponent of convergence of zeros of f . The rst and the second fundamental theorems are main parts of the theory. The rst main theorem gives an upper bound for the counting
1
function N
for any a
2 C and for large r, while the second main theorem
r;
f a
provides a lower bound on the sum of any nite collection of counting functions
1
where a
2 C and large r. In addition the identity
