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Comptes Rendus Mathématique
Volume 335, n° 1
pages 1-4 (2002)
Doi : S1631-073X(02)02424-X
Received : 22 February 2002 ;  accepted : 29 April 2002
Formes linéaires en polyzêtas et intégrales multiples
Linear forms in multiple zeta values and multiple integrals
 

Stéphane Fischler
Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, 75005 Paris, France 

Note présentée par Christophe Soulé

Résumé

Le problème considéré ici est de définir des familles d'intégrales n -uples, munies d'une action de groupe comme dans les travaux de Rhin-Viola [5,6], dont les valeurs soient des formes linéaires, sur le corps des rationnels, en les polyzêtas de poids au plus n . On généralise pour cela les approches de Vasilyev [10] et Sorokin [7], en les reliant par un changement de variables. On décrit aussi une structure de groupe pour une intégrale n -uple qui donne, pour n =2 et n =3, celles obtenues par Rhin et Viola. Pour citer cet article : S. Fischler, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 1-4.

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Abstract

The problem we consider is to define families of n -dimensional integrals, endowed with group actions as in Rhin-Viola's work [5,6], the values of which are linear forms, over the rationals, in multiple zeta values of weight at most n . We generalize Vasilyev's [10] and Sorokin's [7] approaches, and give a change of variables that connects them to each other. We describe a group structure for a n -dimensional integral that specializes, for n =2 and n =3, to the ones obtained by Rhin and Viola. To cite this article: S. Fischler, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 1-4.

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


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