Computation of the monodromy of generalized polylogarithms

Hoang Ngoc Minh; Michel Petitot; Joris Van Der Hoeven

doi:10.1145/281508.281640

Computation of the monodromy of generalized polylogarithms

Hoang Ngoc Minh
, Michel Petitot
, Joris Van Der Hoeven

Université de Lille

Résultats de recherche: Contribution à une conférence › Papier › Revue par des pairs

Résumé

Generalized polylogarithms (in our sense) are defined as iterated integrals with respect to the two differential forms w₀ = dz/z and w₁ = dz/(1 - z). 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.

langue originale	Anglais
Pages	276-283
Nombre de pages	8
Les DOIs	https://doi.org/10.1145/281508.281640
état	Publié - 1 janv. 1998
Modification externe	Oui
Evénement	Proceedings of the 1998 23rd International Symposium on Symbolic and Algebraic Computation, ISSAC-98 - Rostock, DEU Durée: 13 août 1998 → 15 août 1998

Une conférence

Une conférence	Proceedings of the 1998 23rd International Symposium on Symbolic and Algebraic Computation, ISSAC-98
La ville	Rostock, DEU
période	13/08/98 → 15/08/98

Accès au document

10.1145/281508.281640

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abstract = "Generalized polylogarithms (in our sense) are defined as iterated integrals with respect to the two differential forms w0 = dz/z and w1 = dz/(1 - z). 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.",

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AU - Minh, Hoang Ngoc

AU - Petitot, Michel

AU - Van Der Hoeven, Joris

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N2 - Generalized polylogarithms (in our sense) are defined as iterated integrals with respect to the two differential forms w0 = dz/z and w1 = dz/(1 - z). 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.

AB - Generalized polylogarithms (in our sense) are defined as iterated integrals with respect to the two differential forms w0 = dz/z and w1 = dz/(1 - z). 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.

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T2 - Proceedings of the 1998 23rd International Symposium on Symbolic and Algebraic Computation, ISSAC-98

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Computation of the monodromy of generalized polylogarithms

Résumé

Une conférence

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