Some Researches On L-Functions In The Extended Selberg Class And Complex Differential-Difference Equations

Value distribution theory of meromorphic functions,due to R.Nevanlinna in the early 20th century,the theory has become the main tool to study the uniqueness of meromorphic functions,but also has important applications in other research associ-ated with meromorphic functions.For example,the theory of complex differential-difference equations.In this paper,we research the uniqueness of L-functions in the extend Selberg class and the solution of a certain class of complex differential-difference equations by using the value distribution theory as an important tool.Paper is divided into five chapters,the concrete arrangement is as follows:In chapter 1,we briefly introduce the value distribution theory of meromorphic functions,L-functions in Selberg class,the difference version of Nevanlinna theory and the uniqueness theory of meromorphic functions.In chapter 2,firstly,we complement the existing uniqueness results of L-functions in the extended Selberg class by changing the sharing situation of sharing values.Secondly,in view of sharing sets,we obtain new results on the uniqueness of L-functions in the extended Selberg class,which further improve the uniqueness theory of L-functions in the extended Selberg class.In chapter 3,relying on Nevanlinna theory and the properties of L-functions in the extended Selberg class,we mainly study the uniqueness problems on L-functions concerning certain differential polynomials.This generalizes some results of Liu-Li-Yi.Meanwhile,we give some examples to demonstrate that the conditions are necessary.In chapter 4,we study a class of nonlinear complex differential-difference equation fn+pd(z,f)=ple?1z+p2e?2z,n?2,which complements some previous results.In chapter 5,we make a summary and present some problems.