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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.

##### 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
##### Keywords:
monodromy; shuffle algebra
AXIOM
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