AUTOMORPHISM OF SOLUTIONS TO RAMANUJAN'S DIFFERENTIAL EQUATIONS AND OTHER RESULTS

Abstract

In part one we prove a theorem about the automorphism of solutions to Ramanujan's differential equations. We also establish the relationship to solutions given by Lamé's equation and 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 generalized Chazy equation with parameter k = 3/2.