Meromorphic continuation of Multivariable Euler product and application

2005/02/24 by Gautami Bhowmik, Bhowmik, Gautami, Driss Essouabri +3
Mathematics · #11N37 #14G05 #32D15 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #MSC 11M41 #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0502508

openalex publication_date 2005/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \Cⁿ. Among applications we deduce analytic properties of height zeta functions for toric varieties over \Q and group zeta functions.

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• Explicit Analytic Continuation of Euler Products
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