Double shuffle relations for q-analogues of multiple zeta values, their derivatives and the connection to multiple Eisenstein series

TL;DR

This paper investigates q-analogues of multiple zeta values linked to Eisenstein series, exploring their algebraic properties, derivatives, and proposing explicit formulas for derivatives of double and triple Eisenstein series.

Contribution

It introduces conjectured explicit formulas for derivatives of multiple Eisenstein series based on the algebraic structure of q-analogues of multiple zeta values.

Findings

Proposed conjectured formulas for derivatives of Eisenstein series

Analysis of algebraic structure of q-analogues of multiple zeta values

Connection established between q-analogues and multiple Eisenstein series

Abstract

We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the derivatives of double and triple Eisenstein series.