Relations between values at T-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables - Université de La Réunion Access content directly
Journal Articles Journal of the Mathematical Society of Japan Year : 2008

Relations between values at T-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables

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.

Dates and versions

hal-01186185 , version 1 (24-08-2015)

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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. Journal of the Mathematical Society of Japan, 2008, 60 (1), pp.1-16. ⟨10.2969/jmsj/06010001⟩. ⟨hal-01186185⟩
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