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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.

11G55Polylogarithms and relations with $K$-theory
16S99Associative rings and algebras arising under various constructions
11M32Multiple Dirichlet series, etc.
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