ARI/GARI, la dimorphie et l'arithmétique des multizêtas : un premier bilan
Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 2, p. 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}.

@article{JTNB_2003__15_2_411_0,
     author = {\'Ecalle, Jean},
     title = {ARI/GARI, la dimorphie et l'arithm\'etique des multiz\^etas : un premier bilan},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {2},
     year = {2003},
     pages = {411-478},
     zbl = {02184608},
     mrnumber = {2140864},
     language = {fr},
     url = {http://www.numdam.org/item/JTNB_2003__15_2_411_0}
}
Ecalle, Jean. 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. http://www.numdam.org/item/JTNB_2003__15_2_411_0/

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