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 = {Henri Cohen}, 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}, doi = {10.5802/jtnb.285}, zbl = {0976.11055}, mrnumber = {1823191}, language = {fr}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.285/} }
TY - JOUR TI - Comptage exact de discriminants d'extensions abéliennes JO - Journal de Théorie des Nombres de Bordeaux PY - 2000 DA - 2000/// SP - 379 EP - 397 VL - 12 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.285/ UR - https://zbmath.org/?q=an%3A0976.11055 UR - https://www.ams.org/mathscinet-getitem?mr=1823191 UR - https://doi.org/10.5802/jtnb.285 DO - 10.5802/jtnb.285 LA - fr ID - JTNB_2000__12_2_379_0 ER -
Henri Cohen. Comptage exact de discriminants d'extensions abéliennes. Journal de Théorie des Nombres de Bordeaux, Volume 12 (2000) no. 2, pp. 379-397. doi : 10.5802/jtnb.285. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.285/
[1] A course in computational algebraic number theory (third printing). Graduate Texts in Math. 138, Springer-Verlag (1996). | MR: 1228206 | Zbl: 0786.11071
,[2] Advanced topics in computational number theory. Graduate Texts in Math 193, Springer-Verlag (2000). | MR: 1728313 | Zbl: 0977.11056
,[3] Densité des discriminants des extensions cycliques de degré premier, C.R. Acad. Sci. Paris 330 (2000), 61-66. | MR: 1745187 | Zbl: 0941.11042
, , ,[4] Counting discriminants of number fields of degree up to four. proceedings ANTS IV Leiden (2000), Lecture Notes in Comp. Sci. 1838, Springer-Verlag, 269-283. | MR: 1850611 | Zbl: 0987.11080
, , ,[5] Counting discriminants of number fields. MSRI preprint 2000-026 (2000), 9p.
, , ,[6] Asymptotic and exact enumemtion of discriminants of number fields. En préparation.
, , ,[7] Enumerating quartic dihedral extensions of Q. Submitted.
, , ,[8] On the density of discriminants of cyclic extensions of prime degree. En préparation.
, , ,[9] On the density of discriminants of quartic number fields. En préparation.
, , ,[10] Explicit estimates for summatory functions linked to the Möbius μ- function. Preprint (1996), soumis.
, , ,[11] Computing the summation of the Möbius function. Exp. Math. 5 (1996), 291-295. | EuDML: 229511 | MR: 1437219 | Zbl: 1007.11083
, ,[12] Introduction à la théorie analytique et probabiliste des nombres. Cours Spécialisé S.M.F. 1, Paris (1996). | MR: 1366197 | Zbl: 0880.11001
,Cited by Sources: