New proofs of two identities of Ramanujan

Abstract

A proof of several identities of Ramanujan involving theta functions of level $7$ is given which uses a specific modular function for ${\Gamma }_1(7)$ and Klein's projective representation of $PSL(2,7)$ into $PSL(3,\mathbb{C})$. Four identities of Berndt and Zhang are derived as algebraic corollaries of the main proof.

arXiv comment20 pages. Section 4 has been added, giving corollaries of the main proof. Title has been modified