Elliptic multiple zeta values and the elliptic double shuffle relations

Pierre Lochak, Nils Matthes, Leila Schneps

Published 2017-03-28Version 1

We study the algebra $\mathcal{E}$ of elliptic multiple zeta values, which is an elliptic analog of the algebra of multiple zeta values. We identify a set of generators of $\mathcal{E}$, which satisfy a double shuffle type family of algebraic relations, similar to the double-shuffle relations for multiple zeta values. We prove that the elliptic double shuffle relations give all algebraic relations among elliptic multiple zeta values, if (a) the classical double shuffle relations give all algebraic relations among multiple zeta values and if (b) the elliptic double shuffle Lie algebra has a certain natural semi-direct product structure.