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

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

2011-07-02

arxiv.org/abs/1107.0413v1

Mathematics

Number Theory

22 pages, To appear in International Journal of Number Theory

Scientific paper

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.

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