Arborified multiple zeta values
Combinatorics
2019-12-12 v1 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1603.01498,
title = {Arborified multiple zeta values},
author = {Dominique Manchon},
journal= {arXiv preprint arXiv:1603.01498},
year = {2019}
}
Comments
From a talk at the ESF exploratory workshop "New approaches to Multiple Zeta Values", ICMAT, Madrid, Sept-Oct. 2013