 |
|
Computing Polynomials of the Ramanujan $t_n$ Class Invariants |
Canad. Math. Bull. 52(2009), 583-597
Published:2009-12-01
Printed: Dec 2009
Printed: Dec 2009
- Elisavet Konstantinou
- Aristides Kontogeorgis
Abstract
We compute the minimal polynomials of the Ramanujan values $t_n$,
where $n\equiv 11 \mod 24$, using the 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.
| MSC Classifications: |
11R29 - Class numbers, class groups, discriminants 33E05 - Elliptic functions and integrals 11R20 - Other abelian and metabelian extensions |