Some Results On The Unique Rangesets Of Meromorphic Functions

The main content researched in this thesis is the application of the uniqueness of meromorphic functions involving shared value sets in the value distribution theory of meromorphic functions.These studies on the unique range sets of meromorphic functions expand and improve the several previous results.The main conclusions as follows:Let f(z)and g(z)be nonconstant meromorphic functions in the complex plane.(1)If the positive number ?<1/4,N(r,f)+N(r,g)??(T(r,f)+T(r,g))+S(r,f)+S(r,g),N(r,1/f)?m(r,1/f)+S(r,f),f(z)and g(z)share the set{z:z6+z5+1=0}CM Then f(z)?g(z).(2)If ? is some positive number and 0<?<1,S={1,?1,…,?7} is a set of different zeros of polynomial P(z)=36z10-80z9+45z8-1,the specific form of mapping ?:-S?N+ is?(1)=3,?(?k)=1(k=1,…,7),f(z)and g(z)share the set S CM With ?:S?N+ as weight function,and ?(?,f)>?,?(?,g)>?.Then f(z)?g(z).(2)If pk(k=1,…,5)are positive integers of mutual prime,(?){pk}?4,aj(j=1,…,5)are finite complex numbers and different from each other,the specific form of?:S?N+ is ?(ak)=pk(k=1,…,5),f(z)and g(z)share the set S CM with?:S?N+ as weight function.Then there must be f(z)?g(z).