Unramified quaternion extensions of quadratic number fields
Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 1, pp. 51-68.

Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields k correspond to certain factorizations of its discriminant disc k. In this paper we extend their results to unramified quaternion extensions of k which are normal over , and show how to construct them explicitly.

Des résultats classiques dûs à Rédei, Reichardt et Scholz montrent que les extensions cycliques non ramifiées de degré 4 d’un corps de nombre quadratique k correspondent à certaines factorisations du discriminant disc k. Dans cet article, on généralise ces résultats aux extensions quaternionniennes non ramifiées et galoisiennes sur . On montre aussi comment les construire explicitement.

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Franz Lemmermeyer. Unramified quaternion extensions of quadratic number fields. Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 1, pp. 51-68. doi : 10.5802/jtnb.189. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.189/

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