The algorithmic and combinatorial aspects of functional equations on polylogarithms

Hoang Ngoc Minh

University of Lille 2 - CNRS (France)

March 13,
refreshments at 3:45pm


The algebra of polylogarithms is the smallest C-algebra that contains the constants and that is stable under integration with respect to the differential forms dz/z and dz/(1-z). It is known that this algebra is isomorphic to the algebra of the noncommutative polynomials equipped with the shuffle product. As a consequence, the polylogarithms Li_n(g(z)), where the g(z) belong to the group of biratios, are polynomial on the polylogarithms indexed by Lyndon words with coefficients in a certain transcendental extension of Q : MZV, the algebra of the Euler-Zagier sums. The question of knowing whether the polylogarithms Li_n(g(z)) satisfy a linear functional equation is then effectively decidable up to a construction of a basis for the algebra MZV.

Speaker's Contact Info: hoang(at-sign)

Return to seminar home page

Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

Page loaded on March 07, 2002 at 11:21 AM. Copyright © 1998-99, Sara C. Billey. All rights reserved.