Analytic continuation of multivariable Dirichlet series

Abstract:

We will present various analytical tools to study the holomorphic (or meromorphic) continuation of multivariate Dirichlet series, especially powerful for polyhedral domains of extension. These tools will be applied to several examples from combinatorics and number theory, in particular the determination of the maximal domain of meromorphic continuation for Dirichlet series representable as Euler products.

Joint work with Oswaldo Velásquez Castañón