Arborified multiple zeta values

Dominique Manchon (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We describe some particular finite sums of multiple zeta values which arise from J. Ecalle’s “arborification”, a process which can be described as a surjective Hopf algebra morphism from the Hopf algebra of decorated rooted forests onto a Hopf algebra of shuffles or quasi-shuffles. This formalism holds for both the iterated sum picture and the iterated integral picture. It involves a decoration of the forests by the positive integers in the first case, by only two colours in the second case.

Mots clés: multiple zeta values; rooted trees; Hopf algebras; shuffle; quasi-shuffle; arborification

Domaines: Mathématiques [math]; Combinatoire [math.CO]

Dominique Manchon. Arborified multiple zeta values. Jose Ignacio Burgos Gil, Kurusch Ebrahimi-Fard, Herbert Gangl. Periods in Quantum Field Theory and Arithmetic, 314, Springer, pp.469-481, 2020, Springer Proceedings in Mathematics & Statistics book series, 978-3-030-37030-5. ⟨hal-02404060⟩