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In this paper, we obtain some new Eisenstein series identities containing the Borweins' cubic theta functions using (p, k)-parameterization. Further, as an application of this, we evaluate the convolution sum ∑ i + 4 j = n σ (i) σ (j) . [ABSTRACT FROM AUTHOR]

S. Ramanujan has recorded many theta-function identities in his notebooks and 'Lost' notebook. Inspired by the works of Ramanujan, recently M. Somos discovered several new theta-function identities using PARI/GP scripts without offering the proof, which are analogous to Ramanujan's theta-function identities. In this paper, we give proofs for some theta-function identities of level 8 discovered by Somos. Furthermore, we extract some partition identities from them. [ABSTRACT FROM AUTHOR]