Double shuffle relations for arborified zeta values

Abstract

Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to relate them to multizeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborifed zeta values are algebra morphisms for these new products on trees.

arXiv commentMatch the version to be published in Journal of Algebra. One diagram added, minor modifications

References in corpus (7)

• Multiple zeta-star values and multiple integrals
• Multiple zeta values and periods of moduli spaces ${\mathfrak{M}}_{0,n}$
• Renormalization and Mellin transforms
• Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes
• A comodule-bialgebra structure for word-series substitution and mould composition
• Explicit formulas of Euler sums via multiple zeta values
• Locality and renormalisation: universal properties and integrals on trees