×

zbMATH — the first resource for mathematics

Shuffle algebra and polylogarithms. (English) Zbl 0965.68129
Summary: Generalized polylogarithms are defined as iterated integrals with respect to the two differential forms \(\omega_0= dz/z\) and \(\omega_1= dz/(1- z)\). We give an algorithm which computes the monodromy of these special functions. This algorithm, implemented in AXIOM, is based on the computation of the associator \(\Phi_{KZ}\) of Drinfel’d, in factorized form. The monodromy formulae involve special constants, called multiple zeta values. We prove that the algebra of polylogarithms is isomorphic to a shuffle algebra.

MSC:
11G55 Polylogarithms and relations with \(K\)-theory
16S99 Associative rings and algebras arising under various constructions
11M32 Multiple Dirichlet series and zeta functions and multizeta values
Software:
AXIOM
PDF BibTeX XML Cite
Full Text: DOI