Shuffle algebra and polylogarithms


Generalized polylogarithms are defined as iterated integrals with respect to the two differential forms and . We prove an algorithm which computes the monodromy of these special functions. This algorithm, implemented in Axiom, is based on the Lyndon basis. The monodromy formulae involve special constants, called multiple zeta values. We prove that the algebra of polylogarithms is isomorphic to a shuffle algebra.

Authors: Hoang Ngoc Minh, Michel Petitot, Joris van der Hoeven

Keywords: polylogarithms, multiple zeta values, monodromy, Lyndon words

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