Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals

TL;DR

This paper introduces a decomposition algorithm for elliptic multiple zeta values, mapping them injectively to iterated Eisenstein integrals, and explores the structure of this mapping related to modular form period polynomials.

Contribution

It presents a novel decomposition algorithm for elliptic multiple zeta values and analyzes the image of the associated injective map.

Findings

Constructed an injective map from elliptic multiple zeta values to iterated Eisenstein integrals

Provided numerous examples illustrating the decomposition process

Identified the role of period polynomials in the surjectivity of the map

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.