In the present work, we prove few new Dedekind eta-function identities of level 6 discovered by Somos in two different methods. Also during this process, we give an alternate method to Somos’s Dedekind eta-function identities of level 6 proved by B. R. Srivatsa Kumar et. al. As an application of this, we establish colored partition identities.

<abstract><p>S. Ramanujan documented several modular equations of degrees in his notebooks. These identities are used to evaluate Weber's class in variants, continued fractions and many more. In the present work, we establish modular equations of composite degrees using the known identities.</p></abstract>

Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using ( p , k )-parametrization in terms of Borweins’ theta functions.

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