  In this paper, we initiate a generous amount of new-found general theorems
for explicit evaluations of product of the theta functions $b_{m, n}$ using
Kronecker's limit formula and other various novel explicit evaluations that
were introduced thereupon. Also, we have obtained a few novel values of
Ramanujan's class invariant $g_n$ using new-found values of $b_{m, n}$.
Eventually, we have shown that $b_{m, n}$ is the unit in certain algebraic
number fields.
