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Comptes Rendus Mathématique
Volume 352, n° 11
pages 865-869 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.006
Received : 27 December 2013 ;  accepted : 11 September 2014
The algebra of Hurwitz multizeta functions
Sur l'algèbre des multizêtas de Hurwitz
 

Olivier Bouillot
 Laboratoire d'informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée, Cité Descartes, 5, bd Descartes, 77454 Marne-la-Vallée cedex 2, France 

Abstract

Multizeta values are real numbers that span a complicated algebra: there exist two different interacting products. A functional analog of these numbers is defined so as to obtain a better understanding of them, the Hurwitz multizeta functions, which span an algebra for which a precise description is wanted. In this note, we prove that the algebra of Hurwitz multizeta functions is a polynomial algebra.

The full text of this article is available in PDF format.
Résumé

Les multizêtas sont des nombres réels possédant une structure d'algèbre complexe : il existe deux produits interagissant. Il est naturel de définir un analogue fonctionnel de ces nombres pour en avoir une meilleure compréhension, ce qui conduit aux multizêtas de Hurwitz, dont on souhaiterait connaître précisémment la structure d'algèbre. Dans cette note, nous montrons que l'algèbre des multizêtas de Hurwitz est une algèbre de polynômes.

The full text of this article is available in PDF format.


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