Stuffle regularized multiple Eisenstein series revisited

TL;DR

This paper revisits multiple Eisenstein series, providing a new algebraic interpretation of their stuffle regularization using Hopf algebra structures, bridging modular forms and multiple zeta values.

Contribution

It introduces a novel algebraic perspective on regularized multiple Eisenstein series through Hopf algebra, enhancing understanding of their structure and connections.

Findings

New algebraic interpretation of regularized multiple Eisenstein series

Connection established between harmonic algebra and Eisenstein series

Enhanced framework linking modular forms and multiple zeta values

Abstract

Multiple Eisenstein series are holomorphic functions in the complex upper-half plane, which can be seen as a crossbreed between multiple zeta values and classical Eisenstein series. They were originally defined by Gangl-Kaneko-Zagier in 2006, and since then, many variants and regularizations of them have been studied. They give a natural bridge between the world of modular forms and multiple zeta values. In this note, we give a new algebraic interpretation of stuffle regularized multiple Eisenstein series based on the Hopf algebra structure of the harmonic algebra introduced by Hoffman.