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.
Publié le : 2008-01-15
Classification:
twisted multiple zeta-function,
Analytic continuation,
special values,
11M41,
11R42
@article{1206367952,
author = {DE CRISENOY, Marc and ESSOUABRI, Driss},
title = {Relations between values at $T$ -tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 1-16},
language = {en},
url = {http://dml.mathdoc.fr/item/1206367952}
}
DE CRISENOY, Marc; ESSOUABRI, Driss. Relations between values at $T$ -tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 1-16. http://gdmltest.u-ga.fr/item/1206367952/