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

TL;DR

This paper computes minimal polynomials of Ramanujan values for discriminants congruent to 5 mod 24 using a modified Shimura Reciprocity Law approach that applies to modular functions not necessarily producing class invariants.

Contribution

It introduces a modified computational method based on Shimura Reciprocity Law for Ramanujan values that are not class invariants, expanding the scope of explicit class field computations.

Findings

Computed minimal polynomials for specific discriminants.

Modified method applicable to non-class invariant modular functions.

Enhanced understanding of Ramanujan values for discriminants 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.