On Certain Identities Of Ramanujan Original Research Article

In this paper we will start with one identity of Ramanujan about Lambert series related to modular relations of degree 7 to give some completely new proofs of several important theta functions identities proved by Berndt and Zhang [1994, J. Number Theory48, 224–242] via the theory of modular forms. This study also yields a simple proof of one important identity of Ramanujan connected with partitions modulo 7. We also derive some new theta-function identities.