Geodesic
Some quartic number fields containing an imaginary quadratic subfield
Stéphane R. Louboutin1
1 Institut de Mathématiques de Luminy, UMR 6206 163, avenue de Luminy, Case 907 13288 Marseille Cedex 9, France
Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 139-148.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $\varepsilon$ be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field $K ={\mathbb Q}(\varepsilon)$ to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of $K$ to be equal to ${\mathbb Z}[\varepsilon]$. We also prove that the class number of such $K$'s goes to infinity effectively with the discriminant of $K$.
DOI : 10.4064/cm122-1-13
Keywords: varepsilon quartic algebraic unit necessary sufficient conditions quartic number field mathbb varepsilon contain imaginary quadratic subfield ring algebraic integers equal mathbb varepsilon prove class number goes infinity effectively discriminant nbsp

Stéphane R. Louboutin 1

1 Institut de Mathématiques de Luminy, UMR 6206 163, avenue de Luminy, Case 907 13288 Marseille Cedex 9, France 
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Stéphane R. Louboutin. Some quartic number fields containing
an imaginary quadratic subfield. Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 139-148. doi : 10.4064/cm122-1-13. http://geodesic.mathdoc.fr/articles/10.4064/cm122-1-13/

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