Comptage exact de discriminants d'extensions abéliennes
Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 2, p. 379-397

This paper explains how to compute exactly the number of isomorphism classes of abelian extensions of in degree less than or equal to 4 having their discriminant bounded by a given integer. For example, we are able to compute the number of cyclic cubic fields of discriminant less than or equal to 10 37 .

Le but de cet article est d’expliquer comment calculer exactement le nombre de classes d’isomorphismes d’extensions abéliennes de en degré inférieur ou égal à 4 et de discriminant majoré par une borne donnée. On parvient par exemple à calculer le nombre de corps cubiques cycliques de discriminant inférieur ou égal à 10 37 .

@article{JTNB_2000__12_2_379_0,
     author = {Cohen, Henri},
     title = {Comptage exact de discriminants d'extensions ab\'eliennes},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {2},
     year = {2000},
     pages = {379-397},
     zbl = {0976.11055},
     mrnumber = {1823191},
     language = {fr},
     url = {http://www.numdam.org/item/JTNB_2000__12_2_379_0}
}
Cohen, Henri. Comptage exact de discriminants d'extensions abéliennes. Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 2, pp. 379-397. http://www.numdam.org/item/JTNB_2000__12_2_379_0/

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