Dirichlet series and the Nevanlinna class in infinitely many variables

Abstract: This paper is concerned with Dirichlet series and holomorphic functions in infinitely many variables. We study the function theory of the Nevanlinna class and the Smirnov class in infinitely many variables, including boundary behaviors, homogeneous projections, inner functions and outer functions. Many of our results can be applied in Hardy spaces in infinitely many variables. We also discuss the relationship between Dirichlet series and these holomorphic functions.

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