Meromorphic continuation of Multivariable Euler product and application

Details Meromorphic continuation of Multivariable Euler product and application Meromorphic continuation of Multivariable Euler product and application

2005-02-24

arxiv.org/abs/math/0502508v1

Mathematics

Number Theory

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Scientific paper

This article extends classical one variable results about Euler products defined by integral valued polynomial or analytic functions to several variables. We show there exists a meromorphic continuation up to a presumed natural boundary, and also give a criterion, a la Estermann-Dahlquist, for the existence of a meromorphic extension to $\C^n.$ Among applications we deduce analytic properties of height zeta functions for toric varieties over $\Q$ and group zeta functions.

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