On certain relations among the generating functions for certain quadratic forms

Abstract

The object of this article is to establish the relation between the generating function of the quadratic form $2m^2+2mn+3n^2$ {and} the generating function{s} for the quadratic forms $m^2+mn+n^2$, $m^2+mn+2n^2$, $m^2+mn+4n^2$ and $2m^2+mn+2n^2$. In the process, we deduce certain interesting theta function identities.