On the domain of meromorphy of a multivariate Euler product of Igusa type
Ludovic Delabarre
TL;DR
This paper investigates the maximal domain where certain multivariate Euler products of Igusa type are meromorphic, addressing a problem about their natural boundary and extending to a broader class of Euler products.
Contribution
It introduces and characterizes the maximal domain of meromorphy for multivariate pseudo-uniform Euler products, solving a problem posed by Kurokawa and Ochiai.
Findings
Identified the natural boundary of meromorphy for Igusa-type Euler products
Determined the maximal domain of meromorphy for a class of multivariate Euler products
Extended the analysis to pseudo-uniform Euler products
Abstract
This work is an answer to a problem posed by N. Kurokawa and H. Ochiai concerning the natural boundary of meromorphy of a multivariate Euler product of Igusa type. More generally, we introduce and determine the maximal domain of meromorphy of a class of multivariate pseudo-uniform Euler products.
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