Certain new modular identities for Ramanujan's cubic continued fraction.

In this paper, first we establish some new relations for ratios of Ramanujan’s theta functions. We establish some new general formulas for explicit evaluations of Ramanujan’s theta functions. We also establish new relations connecting Ramanujan’s cubic continued fraction V (q) with four other continued fractions V (q 15), V (q 5/3), V (q 21) and V (q 7/3)

Modular relations for J-invariant and explicit evaluations.

On pages 392 − 393 of his second note book Ramanujan defined J-invariant and recorded 14 values of Jn leaving "J99 as J99 = · · · ". All these values have been proved by using known values of Ramanujan-Weber class invariant Gn. Motivated by this, in this paper we establish modular relations connecting J-invariant Jn with five other J-invariants Jr 2n for r = 3, 5, 7, 11, 13. As an pplication, we find several explicit evaluations of Jn for different values of n. At last we give some relations connecting Ln and Rn for different values of n, where Ln and Rn represent Eisenstein series

Schläfli-type mixed modular equations of degrees 1, 3, n and 3n.

In this paper, we establish several new Schlafli-type mixed modular equations of composite degrees. These equations are analogous to those recorded by Ramanujan in his second notebook. As an application, we establish several new explicit values for the Ramanujan-Weber class invariant Gn for n = 12,48,51,57,3/4,3/16,3/17 and 3/19

Certain modular identities for Ramanujan's cubic continued fraction

In this paper, first we establish some new relations for ratios of Ramanujan's theta functions. We also establish new relations connecting Ramanujan's cubic continued fraction V(q) with three other continued fractions V(q24), V(q8/3) and V(q27)