A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values

Abstract

We present the τ-invariant balanced quasi-shuffle algebra $G^f$, whose elements formalize (combinatorial) multiple Eisenstein series as well as multiple q-zeta values. In particular, $G^f$ has natural maps into these two algebras, and we expect these maps to be isomorphisms. Racinet studied the algebra $Z^f$ of formal multiple zeta values by examining the corresponding affine scheme DM. Similarly, we present the affine scheme BM corresponding to the algebra $G^f$. We show that Racinet's affine scheme DM embeds into our affine scheme BM. This leads to a projection from the algebra $G^f$ onto $Z^f$. Via the above natural maps, this projection corresponds to extracting the constant terms of multiple Eisenstein series or the limit $q\to 1$ of multiple q-zeta values.