Title :

Meromorphic continuation of Multivariable Euler product and application

Author(s) :

Bhowmik, Gautami [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Essouabri, Driss [Auteur]
Laboratoire de Mathématiques Nicolas Oresme [LMNO]
Lichtin, Ben [Auteur]

English keyword(s) :

zeta functions of groups.
several variables zeta functions
Euler product
analytic continuation
Manin's conjecture
Rational points
zeta functions of groups

HAL domain(s) :

Mathématiques [math]/Théorie des nombres [math.NT]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Comment :

article soumis

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL