Differential equations involving cubic theta functions and Eisenstein series

TL;DR

This paper derives systems of differential equations for modular forms of level three, extending Ramanujan's classical Eisenstein series ODEs to a higher level using cubic theta functions.

Contribution

It introduces new differential equations for level three modular forms, generalizing Ramanujan's classical Eisenstein series system.

Findings

Derived ODE systems for level three modular forms

Extended Ramanujan's classical Eisenstein series equations

Connected cubic theta functions with Eisenstein series

Abstract

In this paper, we derive systems of ordinary differential equations (ODEs) satisfied by modular forms of level three, which are level three versions of Ramanujan's system of ODEs satisfied by the classical Eisenstein series.