Ramanujan’s Type of Product of Theta Functions and Its Applications

In this paper, we present several new general theorems for the explicit evaluation of the product of theta function bM,N , employing Kronecker’s limit formula alongside a set of analytical methods developed within this work. Based on these evaluations, we derive new explicit values of Ramanujan’s class invariants gₙ using the computed expressions for bM,N . Furthermore, we demonstrate that bM,N constitutes a unit in certain algebraic number fields.