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Meromorphic continuation of multivariable Euler products
-
Gautami Bhowmik
,
Driss Essouabri
Veröffentlicht/Copyright:
19. November 2007
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 give a criterion, à la Estermann-Dahlquist, for the existence of a meromorphic extension to 
. In addition, we precisely describe the boundaries of analyticity and meromorphy for a multivariable Euler product determined by any toric variety (split over 
). Using our method, we are also able to calculate a precise asymptotic for the number of n-fold products of integers that equal the nth power of an integer, for any n ≥ 3.
Received: 2005-03
Revised: 2006-02
Published Online: 2007-11-19
Published in Print: 2007-11-20
© Walter de Gruyter
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- Derivations of multi-loop algebras
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Artikel in diesem Heft
- On the simple connectedness of certain subsets of buildings
- A generalization of Kronecker function rings and Nagata rings
- Cotilting and tilting modules over Prüfer domains
- Derivations of multi-loop algebras
- Injective and colon properties of ideals in integral domains
- A Lewis Correspondence for submodular groups
- Spreads of PG(3, q) and ovoids of polar spaces
- Meromorphic continuation of multivariable Euler products
