Comptes Rendus
no. 1
Formes linéaires en polyzêtas et intégrales multiples
Stéphane Fischler1
1 Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, 75005 Paris, France
Comptes Rendus. Mathématique, Volume 335 (2002) no. 1, pp. 1-4.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02424-X

Stéphane Fischler 1

1 Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, 75005 Paris, France 
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Stéphane Fischler. Formes linéaires en polyzêtas et intégrales multiples. Comptes Rendus. Mathématique, Volume 335 (2002) no. 1, pp. 1-4. doi : 10.1016/S1631-073X(02)02424-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02424-X/

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