Ramanujan Invariants for discriminants congruent to $\mathbf{5\;mod \;24

Abstract

In this paper we compute the minimal polynomials of Ramanujan values $27t_n^{-12}$ for discriminants D\equiv5mod24. Our method is based on Shimura Reciprocity Law as which was made computationally explicit by A.Gee and P. Stevenhagen. However, since these Ramanujan values are not class invariants, we present a modification of the above method which can be applied on modular functions that do not necessarily yield class invariants.

22 pages, To appear in International Journal of Number Theory