Lyndon words, polylogarithms and the Riemann Zeta function

  title={Lyndon words, polylogarithms and the Riemann Zeta function},
  author={Hoang Ngoc Minh and Michel Petitot},
  journal={Discrete Mathematics},
The algebra of polylogarithms (iterated integrals over two di erential forms !0 = dz=z and !1 = dz=(1 − z)) is isomorphic to the shu e algebra of polynomials on non-commutative variables x0 and x1. The multiple zeta values (MZVs) are obtained by evaluating the polylogarithms at z = 1. From a second shu e product, we compute a Gr obner basis of the kernel of this evaluation morphism. The completeness of this Gr obner basis up to order 12 is equivalent to the classical conjecture about MZVs. We… CONTINUE READING