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.
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Journal of the Mathematical Society of Japan, Maruzen Company Ltd, 2008, 60 (1), pp.1-16. 〈10.2969/jmsj/06010001〉
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http://hal.univ-reunion.fr/hal-01186185
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Soumis le : lundi 24 août 2015 - 14:29:44
Dernière modification le : lundi 23 avril 2018 - 14:51:53

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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, Maruzen Company Ltd, 2008, 60 (1), pp.1-16. 〈10.2969/jmsj/06010001〉. 〈hal-01186185〉

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