Multiple hypergeometric series and polyzetas. (Séries hypergéométriques multiples et polyzêtas.) (French) Zbl 1161.33003

Cresson, J.; Fischler, S.; Rivoal, T.

Bull. Soc. Math. Fr. 136, No. 1, 97-145 (2008).

The authors of this important paper offer a theoretical and effective algorithm for decomposition as linear combinations of multiple zeta values of certain general hypergeometric series and integrals. Such results have a major importance e.g. in the difficult theory of linear independence study of the classical zeta function value. The results are too involved to be stated here.

Reviewer: József Sándor (Cluj-Napoca)

MSC:

11M32	Multiple Dirichlet series and zeta functions and multizeta values
33C70	Other hypergeometric functions and integrals in several variables
11J72	Irrationality; linear independence over a field
33B30	Higher logarithm functions
33C20	Generalized hypergeometric series, \({}_pF_q\)

Keywords:

multiple zeta value; multiple hypergeometric series; algorithm