Automorphism of solutions to Ramanujan's differential equations and other results

TL;DR

This paper proves automorphism theorems for solutions to Ramanujan's differential equations and a related system for the Chazy equation, exploring their mathematical symmetries and potential applications.

Contribution

It introduces new automorphism theorems for solutions of Ramanujan's and Chazy's differential equations, expanding understanding of their symmetries.

Findings

Automorphism theorem for Ramanujan's differential equations

Automorphism theorem for Chazy's equation system

Potential applications of these automorphisms

Abstract

In part one we prove a theorem about the automorphism of solutions to Ramanujan's differential equations. We also investigate possible applications of the result. In part two we prove a similar theorem about the automorphism of solutions to the first-order system of differential equations associated to the generalised Chazy equation with parameter $k=\frac{3}{2}$.