Pré-Publication, Document De Travail Année : 2005

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

Résumé

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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hal-00004986 , version 1 (26-05-2005)

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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.. 2005. ⟨hal-00004986⟩
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