no. 4
Statistics of genus numbers of cubic fields
[Statistiques des nombres de genres sur des corps cubiques]
McGown, Kevin J.1 ; Tucker, Amanda2
1 California State University, Chico (USA)
2 University of Rochester (USA)
Annales de l'Institut Fourier, Tome 73 (2023) no. 4, pp. 1365-1383.

Nous prouvons qu’il y a approximativement 96.23% de corps de nombres cubiques, ordonnés par discriminant, dont le nombre de genres est un et nous calculons la proportion exacte des corps de nombres cubiques avec un nombre de genres donné. Nous calculons également le nombre de genres moyen. Finalement, nous montrons qu’il y a une proportion strictement positive de corps de nombres cubiques totalement réels avec un nombre de genres un qui ne sont pas euclidiens pour la norme.

We prove that approximately 96.23% of cubic fields, ordered by discriminant, have genus number one, and we compute the exact proportion of cubic fields with a given genus number. We also compute the average genus number. Finally, we show that a positive proportion of totally real cubic fields with genus number one fail to be norm-Euclidean.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3558
Classification : 11R16, 11R29, 11R45
Keywords: cubic field, genus number, discriminant density, norm-Euclidean
Mot clés : corps cubique, nombre de genres, densité du discriminant, euclidien pour la norme
McGown, Kevin J. 1 ; Tucker, Amanda 2

1 California State University, Chico (USA)
2 University of Rochester (USA)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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McGown, Kevin J.; Tucker, Amanda. Statistics of genus numbers of cubic fields. Annales de l'Institut Fourier, Tome 73 (2023) no. 4, pp. 1365-1383. doi : 10.5802/aif.3558. https://aif.centre-mersenne.org/articles/10.5802/aif.3558/

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