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1. CMB 2011 (vol 56 pp. 148)
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On the Gras Conjecture for Imaginary Quadratic Fields In this paper we extend K. Rubin's methods to prove the Gras conjecture
for abelian extensions of a given imaginary quadratic field $k$ and
prime numbers $p$ that divide the number of roots of unity in $k$.
Keywords:elliptic units, Stark units, Gras conjecture, Euler systems Categories:11R27, 11R29, 11G16 |
2. CMB 2007 (vol 50 pp. 334)
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Determination of Hauptmoduls and Construction of Abelian Extensions of Quadratic Number Fields 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.
Categories:11F03, 11G16, 11R20 |