Some Eisenstein Series Identities Original Research Article

In this paper we use the theory of elliptic functions to provide different proofs of some Eisenstein series identities of Ramanujan from those given in a recent paper by B. C. Berndt, S. Bhargava, and F. G. Garvan (1995, Trans. Amer. Math. Soc.347, 4136–4244). From one of these identities we derive the inversion formula for the Borweins cubic theta functions via Venkatachanliengarʹs method. We also derive some striking Eisenstein series identities associated with the Borweinsʹ cubic theta functions.