Elliptic Modular Graphs, Eigenvalue Equations and Algebraic Identities

TL;DR

This paper derives eigenvalue equations for elliptic modular graphs with five links, revealing new algebraic identities and advancing understanding of their mathematical structure.

Contribution

It introduces eigenvalue equations for specific elliptic modular graphs and uncovers novel algebraic identities among these graphs.

Findings

Eigenvalue equations for elliptic modular graphs with five links.

New algebraic identities between these graphs.

Enhanced understanding of elliptic modular graph structures.

Abstract

We obtain eigenvalue equations satisfied by various elliptic modular graphs with five links where two of the vertices are unintegrated. Solving them leads to several non--trivial algebraic identities between these graphs.