The algorithmic and combinatorial aspects of functional
equations on polylogarithms
Hoang Ngoc Minh
University of Lille 2  CNRS (France)
March 13,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

The algebra of polylogarithms is the smallest Calgebra that
contains the constants and that is stable under integration with
respect to the differential forms dz/z and dz/(1z).
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 EulerZagier 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(atsign)math.mit.edu
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