A Parameter for Ramanujan's Function χ(q)‎ : Its Explicit Values and Applications

Abstract EN

We define a new parameter Ik,n involving quotient of Ramanujan's function χ(q) for positive real numbers k and n and study its several properties.

We prove some general theorems for the explicit evaluations of the parameter Ik,n and find many explicit values.

Some values of Ik,n are then used to find some new and known values of Ramanujan's class invariant Gn.