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arXiv · 1210.1818

Polylogarithms and multiple zeta values from free Rota-Baxter algebras

Li Guo·Bin Zhang
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Abstract

We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara, Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator. We apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single series. We also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.

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Li Guo, Bin Zhang. 2012-10-05. Polylogarithms and multiple zeta values from free Rota-Baxter algebras. https://doi.org/10.1007/s11425-010-4044-1

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