Shuffle algebra and polylogarithms

Hoang Ngoc Minh; Michel Petitot; Joris Van Der Hoeven

doi:10.1016/S0012-365X(00)00155-2

Shuffle algebra and polylogarithms

Hoang Ngoc Minh
, Michel Petitot
, Joris Van Der Hoeven

Université de Lille

Research output: Contribution to journal › Article › peer-review

Abstract

Generalized polylogarithms are defined as iterated integrals with respect to the two differential forms ω₀ = dz/z and ω₁ =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 Φ_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.

Original language	English
Pages (from-to)	217-230
Number of pages	14
Journal	Discrete Mathematics
Volume	225
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(00)00155-2
Publication status	Published - 28 Oct 2000
Externally published	Yes

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title = "Shuffle algebra and polylogarithms",

abstract = "Generalized polylogarithms are defined as iterated integrals with respect to the two differential forms ω0 = dz/z and ω1 =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 ΦKZ 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.",

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AU - Minh, Hoang Ngoc

AU - Petitot, Michel

AU - Van Der Hoeven, Joris

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N2 - Generalized polylogarithms are defined as iterated integrals with respect to the two differential forms ω0 = dz/z and ω1 =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 ΦKZ 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.

AB - Generalized polylogarithms are defined as iterated integrals with respect to the two differential forms ω0 = dz/z and ω1 =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 ΦKZ 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.

UR - https://www.scopus.com/pages/publications/0347467623

U2 - 10.1016/S0012-365X(00)00155-2

DO - 10.1016/S0012-365X(00)00155-2

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VL - 225

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

Shuffle algebra and polylogarithms

Abstract

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