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This paper is associated with Nevanlinna class, Dirichlet series andSzeg\"o's problem in infinitely many variables. As we will see, there is anatural connection between these topics. The paper first introduces theNevanlinna class and the Smirnov class in this context, and generalizes theclassical theory in finitely many variables to the infinite-variable setting.These results applied to Szeg\"o's problem on Hardy spaces in infinitely manyvariables. Moreover, this paper is also devoted to the study of thecorrespondence between the Nevanlinna functions and Dirichlet series.

Nevanlinna class, Dirichlet series and Szeg\"o's problem