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

Abstract

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

27 pages, comments are welcome!

References in corpus (5)

• Multiple $q$-Zeta Values
• q-Multiple Zeta Functions and q-Multiple Polylogarithms
• Quasi-shuffle products revisited
• The Algebra of a q-Analogue of Multiple Harmonic Series
• Duality and (q-)multiple zeta values

Cited by in corpus (1)

• Formal multiple Eisenstein series and their derivations