Geodesic
Determination of Hauptmoduls and Construction of Abelian Extensions of Quadratic Number Fields
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 334-346

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DOI

We obtain Hauptmoduls of genus zero congruence subgroups of the type $\Gamma _{0}^{+}\left( p \right)\,\,:={{\Gamma }_{0}}\left( p \right)+{{w}_{p}}$ , where $p$ is a prime and ${{w}_{p}}$ is the Atkin–Lehner involution. We then use the Hauptmoduls, along with modular functions on ${{\Gamma }_{1}}\left( p \right)$ 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.
DOI : 10.4153/CMB-2007-032-1
Mots-clés : 11F03, 11G16, 11R20 
Chiang-Hsieh, Hung-Jen; Yang, Yifan. Determination of Hauptmoduls and Construction of Abelian Extensions of Quadratic Number Fields. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 334-346. doi: 10.4153/CMB-2007-032-1
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     title = {Determination of {Hauptmoduls} and {Construction} of {Abelian} {Extensions} of {Quadratic} {Number} {Fields}},
     journal = {Canadian mathematical bulletin},
     pages = {334--346},
     year = {2007},
     volume = {50},
     number = {3},
     doi = {10.4153/CMB-2007-032-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-032-1/}
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