Ramanujan and the Modular <i>j</i>-Invariant
Ramanujan and the Modular <i>j</i>-Invariant
Abstract A new infinite product t n was introduced by S. Ramanujan on the last page of his third notebook. In this paper, we prove Ramanujan’s assertions about t n by establishing new connections between themodular jinvariant and Ramanujan’s cubic theory of elliptic functions to alternative bases. We also show …