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January, 2008 Relations between values at T -tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables
Marc DE CRISENOY, Driss ESSOUABRI
J. Math. Soc. Japan 60(1): 1-16 (January, 2008). DOI: 10.2969/jmsj/06010001

Abstract

We give a new and very concise proof of the existence of a holomorphic continuation for a large class of twisted multivariable zeta functions. To do this, we use a simple method of “decalage” that avoids using an integral representation of the zeta function. This allows us to derive explicit recurrence relations between the values at T –tuples of negative integers. This also extends some earlier results of several authors where the underlying polynomials were products of linear forms.

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Marc DE CRISENOY. Driss ESSOUABRI. "Relations between values at T -tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables." J. Math. Soc. Japan 60 (1) 1 - 16, January, 2008. https://doi.org/10.2969/jmsj/06010001

Information

Published: January, 2008
First available in Project Euclid: 24 March 2008

zbMATH: 1198.11076
MathSciNet: MR2392000
Digital Object Identifier: 10.2969/jmsj/06010001

Subjects:
Primary: 11M41 , 11R42

Keywords: analytic continuation , special values , twisted multiple zeta-function

Rights: Copyright © 2008 Mathematical Society of Japan

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Vol.60 • No. 1 • January, 2008
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