Computing polynomials of the Ramanujan ${\mathbf{t}}_{\mathbf{n}}$ class invariants

Abstract

We compute the minimal polynomials of the Ramanujan values $t_n$, where $n\equiv 11\mathrm{mod}24$, using Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field $\mathbb{Q}(\sqrt{-n})$, and have much smaller coefficients than the Hilbert polynomials.

To appear in Canadian Math. Bulletin