The algorithmic and combinatorial aspects of functional
equations on polylogarithms
Hoang Ngoc Minh
University of Lille 2 - CNRS (France)
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)math.mit.edu
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