Some Results In Value Distribution Theory

In this paper we study the normality of holomorphic functions and the Ozawa's problem of the deficiency sums of Wronskian of meromorphic function , which is an important subject in complex analysis. Much work was made on this respect. The present paper is divided into three parts.In chapter one , we state a few usual notations, definitions and basic results in value distribution theory of meromorphic function .In chapter two, we discuss some normal criteria of holomorphic functions and prove the following result:Let Jbea family of holomorphic functions in a domain D, let n0,..., nk be k non-negative integers with n0 + ... + nk > 2 , and exist ni > 1(0 < i < k - 1) . If for every function f(z) F, the zeros of f(z) have multiplicities at least k , and , then F is normal in D.In chapter three, we discuss the Ozawa's problem of the deficienty sums of Wronskian of meromorphic function and prove the following result:Let f(z) be a meromorphic function of finite order λ. Let a1,a2, ... ,an be linearly independent meromorphic functions which are small related to meromorphic function f(z) . L(f) is defined by L(f)=W(a1, a2,..., an, f) , is a set of meromorphic functions of finite order λ and T(r,f) = O(T(r, L(f)) . HereThen, for any positive integer nwhere d = d(n, λ) is a positive constant satisfying...