This paper explains how to compute exactly the number of isomorphism classes of abelian extensions of in degree less than or equal to 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 .
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 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 .
@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}, pages = {379--397}, publisher = {Universit\'e Bordeaux I}, volume = {12}, number = {2}, year = {2000}, mrnumber = {1823191}, zbl = {0976.11055}, language = {fr}, url = {http://archive.numdam.org/item/JTNB_2000__12_2_379_0/} }
TY - JOUR AU - Cohen, Henri TI - Comptage exact de discriminants d'extensions abéliennes JO - Journal de théorie des nombres de Bordeaux PY - 2000 SP - 379 EP - 397 VL - 12 IS - 2 PB - Université Bordeaux I UR - http://archive.numdam.org/item/JTNB_2000__12_2_379_0/ LA - fr ID - JTNB_2000__12_2_379_0 ER -
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://archive.numdam.org/item/JTNB_2000__12_2_379_0/
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