Lecture Content：

In his lost notebook, Srinivasa Ramanujan documented two important Eisenstein series identities intimately connected with fifth-degree modular equations. Historically, one of these identities played a pivotal role in Ramanujan’s derivation of his celebrated congruence for the partition function modulo 5: p(5n + 4) ≡ 0 (mod 5).

Over the past century, the investigation of Ramanujan’s identities has catalyzed significant progress in both modular forms theory and combinatorial analysis. In this presentation, I will introduce novel parametrizations of these two renowned identities through the framework of elliptic functions.

These parametrizations establish a systematic approach with applications in modular forms theory, proving especially valuable for deriving new identities that connect Eisenstein series with the Dedekind eta function. I will present several new results that illustrate the efficacy and broad applicability of this methodology.

Speaker Introduction: