Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals

Abstract

We describe a decomposition algorithm for elliptic multiple zeta values, which amounts to the construction of an injective map $\psi$ from the algebra of elliptic multiple zeta values to a space of iterated Eisenstein integrals. We give many examples of this decomposition, and conclude with a short discussion about the image of $\psi$. It turns out that the failure of surjectivity of $\psi$ is in some sense governed by period polynomials of modular forms.

v2, minor changes

References in corpus (4)

• Elliptic multiple zeta values and one-loop superstring amplitudes
• Multiple Modular Values and the relative completion of the fundamental group of $M_{1,1}$
• Towards multiple elliptic polylogarithms
• Linear independence of indefinite iterated Eisenstein integrals

Cited by in corpus (3)

• Two-loop diagrams in non-relativistic QCD with elliptics
• Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes
• A construction of single-valued elliptic polylogarithms