Several Types Of Zeros That Extend Beyond The Differential Polynomial Of A Meromorphic Function

In this paper,we mainly study the zeros of several types of differential polynomials of meromorphic functions.And obtain some estimates by the reduced counting function,including the estimates of ?f2(f')2-1,?f2(f')n-1 and af2(f(k))n-1,n?2.where f is a meromorphic function,?((?)0)is a small function of f.We also promote some of the existing literatures results.This paper is divided into five chapters.The contents are as follows:The first chapter mainly introduces the background of this problem,the domestic and foreign research status and development trends.In the second chapter,we introduce the theory of symbols and value distribution of Nevanlinna theory used in this paper.The third chapter,we use the reduced counting function to prove a quantitative estimation inequality of?f2(f')2-1,and extend some of the existing literature results.The forth chapter,we consider the zero of ?f2(f')n-1,the correlation inequality estimation is given by using the reduced counting function.And the existing correlation result is improved by using Yamanoi's inequality.The fifth chapter,we consider the estimate of the differential polynomial af2(f(k))n-1,n ?2,n,k are positive integer,where a(z)(?)0 is a small function of f(z)such as T(r,a)= S(r,f).