ARI/GARI, la dimorphie et l'arithmétique des multizêtas : un premier bilan
Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 2, pp. 411-478.

This survey presents a novel structure : the Lie algebra ARI along with its group GARI. It then goes on to sketch some of the advances which ARI/GARI made possible in the field of MZV (multiple zeta values) arithmetics, and what promises it holds for the investigation of the related, but much broader phenomenon of /emph{numerical dimorphy}.

Nous tentons, dans ce survol, de présenter une structure méconnue : l'algèbre de Lie ARI et son groupe GARI. Puis nous montrons quels progrès elle a déjà permis de réaliser dans l'étude arithmético-algébrique des valeurs zêta multiples et aussi quelles possibilités elle ouvre pour l'exploration du phénomène plus général de /emph{dimorphie numérique}.

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Jean Ecalle. ARI/GARI, la dimorphie et l'arithmétique des multizêtas : un premier bilan. Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 2, pp. 411-478. doi : 10.5802/jtnb.410. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.410/

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