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Meromorphic continuation of Multivariable Euler product and application

Gautami Bhowmik·Driss Essouabri·Ben Lichtin
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Abstract

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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Gautami Bhowmik, Driss Essouabri, Ben Lichtin. 2005-02-24. Meromorphic continuation of Multivariable Euler product and application. https://arxiv.org/abs/math/0502508

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