On Eisenstein series, color partition and divisor function

Abstract

Ramanujan recorded Eisenstein series identities of level 5 of weight 2. The objective of this article is to prove these identities by classical method and also we find some new Eisenstein series identities for level 7. Finally we make use of these results to obtain convolution sums of divisor functions. We will also be introducing certain restricted color partition functions which helps us to represent the convolution sums in a much elegant form than the existing ones.