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

Research output: Contribution to conference › Paper › peer-review

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.

Original language	English
Pages	276-283
Number of pages	8
DOIs	https://doi.org/10.1145/281508.281640
Publication status	Published - 1 Jan 1998
Externally published	Yes
Event	Proceedings of the 1998 23rd International Symposium on Symbolic and Algebraic Computation, ISSAC-98 - Rostock, DEU Duration: 13 Aug 1998 → 15 Aug 1998

Conference

Conference	Proceedings of the 1998 23rd International Symposium on Symbolic and Algebraic Computation, ISSAC-98
City	Rostock, DEU
Period	13/08/98 → 15/08/98

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10.1145/281508.281640

Cite this

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title = "Computation of the monodromy of generalized polylogarithms",

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.",

author = "Minh, \{Hoang Ngoc\} and Michel Petitot and \{Van Der Hoeven\}, Joris",

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doi = "10.1145/281508.281640",

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T1 - Computation of the monodromy of generalized polylogarithms

AU - Minh, Hoang Ngoc

AU - Petitot, Michel

AU - Van Der Hoeven, Joris

PY - 1998/1/1

Y1 - 1998/1/1

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.

U2 - 10.1145/281508.281640

DO - 10.1145/281508.281640

M3 - Paper

AN - SCOPUS:0032514330

SP - 276

EP - 283

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

Y2 - 13 August 1998 through 15 August 1998

ER -

Computation of the monodromy of generalized polylogarithms

Abstract

Conference

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