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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
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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 {\it 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. 2005-05-26. Relations between values at $T$-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables. https://arxiv.org/abs/math/0505568

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