Séries hypergéométriques multiples et polyzêtas

@article{Cresson2006SriesHM,
  title={S{\'e}ries hyperg{\'e}om{\'e}triques multiples et polyz{\^e}tas},
  author={Jacky Cresson and St'ephane Fischler and Tanguy Rivoal},
  journal={Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  year={2006},
  volume={136},
  pages={97-145}
}
Nous decrivons un algorithme theorique et effectif permettant de demontrer que des series et integrales hypergeometriques multiples relativement generales se decomposent en combinaisons lineaires a coefficients rationnels de polyzetas. 
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References

SHOWING 1-10 OF 50 REFERENCES
Approximants de Padé et séries hypergéométriques équilibrées
Resume Dans cet article, nous enoncons et resolvons des problemes d'approximation de Pade nouveaux et tres generaux dont les solutions s'expriment a l'aide de series hypergeometriques : parExpand
Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents
© Association des collaborateurs de Nicolas Bourbaki, 2000-2001, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditionsExpand
Phénomènes de symétrie dans des formes linéaires en polyzêtas
Abstract We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann ζ function at odd integers are irrational.Expand
Well-poised hypergeometric service for diophantine problems of zeta values | NOVA. The University of Newcastle's Digital Repository
On montre comment les concepts classiques de series et integrales hypergeometriques bien equilibrees devient crucial dans l'etude des proprietes arithmetiques des valeurs de la fonction zeta deExpand
La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs
Resume Nous montrons que la dimension de l'espace vectoriel engendre sur les rationnels par 1 et les n premieres valeurs de la fonction zeta de Riemann aux entiers impairs croit au moins comme unExpand
Hypergéométrie et fonction zêta de Riemann
Introduction et plan de l'article Arriere plan Les resultats principaux Consequences diophantiennes du Theoreme $1$ Le principe des demonstrations des Theoremes $1$ a $6$ Deux identites entre uneExpand
Doubles mélanges des polylogarithmes multiples aux racines de l’unité
RésuméRésumé. – Les valeurs des fonctions zêta multiples aux entiers strictement positifs fournissent une solution au système d’équations des associateurs de Drinfel’d, aux nombreuses applications enExpand
Multiple polylogarithms and mixed Tate motives
We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives over a ring of integers in a number field. DescribeExpand
Series generatrices non-commutatives de polyzetas et associateurs de drinfel'd
Dans cette these, on etudie les relations algebriques sur le corps des nombres rationnels entre les nombres polyzetas (generalisations a plusieurs indices des valeurs de la fonction zeta de riemannExpand
Shuffle algebra and polylogarithms
TLDR
It is proved that the algebra of polylogarithms is isomorphic to a shue algebra, and the monodromy formulae involve special constants, called multiple zeta values. Expand
...
1
2
3
4
5
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