Evaluations of certain theta functions in Ramanujan theory of alternative modular bases

Abstract

We give evaluations of certain Borwein's theta functions which appear in Ramanujan theory of alternative elliptic modular bases. Most of this theory where developed by B.C. Berndt, S. Bhargava and F.G. Garvan. We also study the most general class of these theta functions and give evaluation theorems and conjectures.