Uniqueness Of L-functions Concerning Sharing Sets

In 1925,the famous mathematician R.Nevanlinna established the Nevanlinna theory of meromorphic functions,leading the nearly hundred years,the rapid development of the value distribution theory of meromorphic functions.Especially the past30 years,many famous complex analysis experts both at home and abroad,Yang Le,Gross F.,C.C.Yang,P.Li,Fujimoto H.,Min Ru,H.X.Yi and P.C.Hu etc.,using Nevanlinna theory research to the problem of the uniqueness of meromorphic functions solved many classic open issues and derived a lot of uniqueness problem research direction.With the deepening of the famous Riemann hypothesis question research,mathematical workers in recent years to expand the concept of Riemann function,opened up a new class of Dirichlet series,L-function and generalized L-function,and obtains the value distribution of a number of interesting results.This paper is mainly on the basis of predecessors’ research,with the help of the uniqueness theory of meromorphic functions continue to study generalized L-function and general meromorphic function has the share the uniqueness of the collection.The paper is divided into the following four chapters:In chapter 1: Preliminary knowledge.The basic theory of Nevanlinna,the definition of L-function and some commonly used symbols are briefly described,and the related research results of the uniqueness theory of meromorphic function and L-function are introduced.In chapter 2: The uniqueness of L-functions with two Shared sets is studied.The uniqueness of L-functions with two Shared sets of general meromorphic functions is studied and the results partly improved the results of Yi bin,Su min,Lin wei-chuan,Lin pei-qiang et al.In chapter 3: The uniqueness of L-functions with a Shared set is studied.Under some conditions of pole-points or zero-points,the uniqueness of L-functions with a meromorphic functions sharing a set is studied.In chapter 4: The summary and prospect.The research content and results of this paper are analyzed and summarized,and the next research questions and ideas are proposed.