About The Zeros Of Two Types Of Differential Polynomials

In this paper,we consider the value distribution of the differential polynomials ?fn(z)f'(z)-1 and f2(z)(f(z))2-1,where f is a transcendental meromorphic function and ? is a small func-tion,and obtain a precise inequality by the reduced counting function.And we improved the results of some authors.The first chapter is occupied by historical exposition and the course of development around value distribution theory.The second chapter introduces basics and preliminaries,including Nevanlinna charateris-tics and Nevanlinna fundamental theorem.The third chapter is devoted to studying the value distribution of ?fn(z)f'(z)-1,and obtain a precise inequality by the reduced counting function.That is:where n ?2,f(z)is transcendental meromorphic function,? is the small function of f.Thus,the results of papers([7][9][11][25][26])are established and proved.The fourth chapter is devoted to studying the value distribution of f2(z)(f(z))2-1 for k as an integer,where f(z)is a transcendental meromorphic function.We obtain a precise inequality by the reduced counting function:From above inequality,we get the results of value distribution related to the conjecture of the paper[12].Then we study the value distribution of ff(k)and get the following inequality.T(r,f)<6[N,1/ff(k)-1)+N(r,1/ff(k)+1)+S(r,f).And the results of papers([13][14][15][22])are established and proved.