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Search: MSC category 11G16 ( Elliptic and modular units [See also 11R27] )

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1. CMB 2011 (vol 56 pp. 148)

Oukhaba, Hassan; Viguié, Stéphane
 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 systemsCategories:11R27, 11R29, 11G16

2. CMB 2007 (vol 50 pp. 334)

Chiang-Hsieh, Hung-Jen; Yang, Yifan
 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