Cubic and quintic analogues of Ramanujan's septic theta function identity

Abstract

On page 206 in his lost notebook, Ramanujan recorded an incomplete septic theta function identity. Motivated by the completion of this identity by the second author, we offer cubic and quintic analogues. Using the theory generated by these two analogues and Ramanujan's class invariants, we provide many evaluations for Ramanujan's most prominent theta function, $\phi (q)$ in his notation.

33 pages, submitted

References in corpus (1)

• The three missing terms in Ramanujan's septic theta function identity