Some Results Of Meromorphic Functions With Shared Values And Shared Value Sets

A frontier research topic in the field of contemporary uniqueness theory is the study of the uniqueness theory of meromorphic functions.Starting with the five valued theorem proved by the famous Finnish mathematician R.Nevanlinna,it was called the favorite theorem by American mathematician LeeA.Rubel.Then it attracted extensive attention of many scholars,including famous mathematicians,such as C.C.Yang,E.Muse,G.G.Gundersen and so on.To study the uniqueness of meromorphic functions,the important tool is shared value and shared value set.This paper mainly studies the relationship between two functions with shared value and shared value set.This thesis mainly uses the theory of value distribution,and studies two aspects of the uniqueness of functions,on the one hand,whether the number of shared values can be reduced when meromorphic functions have shared values and whether the type condition of the shared value can be weakened,on the other hand,when the entire function has a set of shared values,the number of elements of the set can be less than 7,and the following main conclusions are obtained:1)If the nonconstant meromorphic functions f(z)and f(k)(z)(k is a positive integer)share CM with 0 and IM with a finite complex a different from zero,?(?,f)+?-(0,f)>2-1/(10k+16),then f(z)? f(k)(z).2)If f(z)and g(z)are transcendental meromorphic functions,f(k)(z)and G(k)(z)share IM with 1,?(?,f)= ?(?,g)= 1,3?-(0,f)+5?(0,g)>7,then f(z)? g(z)or f(k)(z)g(k)(z)?1.3)Let n be an integer of n?6,c is a finite complex(where c ?0,1),let P(?)=((n-1)(n-2))/2-n(n-2)?n-1+n(n-1)/2?n-2-c,f(z)and g(z)are nonconstant entire functions.If f(z)and g(z)share the value set of CM with S={??C|P(?)= 0} and(P(f(z)))' and(P(g(z))' share 0 as CM,then f(z)? g(z).