Poisson equations for elliptic modular graph functions

TL;DR

This paper derives Poisson equations for elliptic modular graph functions with four links, revealing new algebraic relations among these functions through detailed analysis.

Contribution

It introduces specific Poisson equations for elliptic modular graph functions with four links, uncovering novel algebraic relations among them.

Findings

Derived Poisson equations for elliptic modular graph functions.

Discovered non-trivial algebraic relations between different graphs.

Enhanced understanding of the structure of elliptic modular graph functions.

Abstract

We obtain Poisson equations satisfied by elliptic modular graph functions with four links. Analysis of these equations leads to a non--trivial algebraic relation between the various graphs.