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Determination of Hauptmoduls and Construction of Abelian Extensions of Quadratic Number Fields |
Canad. Math. Bull. 50(2007), 334-346
Published:2007-09-01
Printed: Sep 2007
Printed: Sep 2007
- Hung-Jen Chiang-Hsieh
- Yifan Yang
Abstract
We obtain Hauptmoduls of genus zero congruence
subgroups of the type $\Gamma_0^+(p):=\linebreak\Gamma_0(p)+w_p$, where $p$ is
a prime and $w_p$ is the Atkin--Lehner involution. We then use the
Hauptmoduls, along with modular functions on $\Gamma_1(p)$
to construct families of cyclic extensions of quadratic number
fields. Further examples of cyclic extension of bi-quadratic and
tri-quadratic number fields are also given.
| MSC Classifications: |
11F03 - Modular and automorphic functions 11G16 - Elliptic and modular units [See also 11R27] 11R20 - Other abelian and metabelian extensions |