Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants

Details Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants

2006-10-11

arxiv.org/abs/math/0610372v1

Mathematics

Number Theory

To appear in Canadian Math. Bulletin

Scientific paper

We compute the minimal polynomials of the Ramanujan values $t_n$, where
$n\equiv 11 \mod 24$, 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.

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