Abstract: This talk is associated with Nevanlinna class, Dirichlet series and Szego's problem in infinitely many variables. As we will see, there is a natural connection between these topics. We first introduce the Nevanlinna class and the Smirnov class in this context, and generalizes the theory of these functions in finitely many variables to version of infinitely many variables. We also apply these results to Szego's problem on Hardy spaces in infinitely many variables. Furthermore, we are also devoted to studying the correspondence between the Nevanlinna functions and Dirichlet series.  This is a joint work with J.Ni and Q.Zhou.