Nous prouvons l’existence d’un sous–ensemble, de densité positive, d’entiers sans facteur carré, tels que le –rang du groupe de classes d’idéaux de vaut . On a désigné par le nombre de diviseurs premiers de l’entier qui sont congrus à modulo . Rappelons que, pour les groupes de classes associés à et , un sous–ensemble analogue d’entiers n’existe pas.
We prove the existence of a subset, with positive natural density, of squarefree integers such that the –rank of the ideal class group of is , where is the number of prime divisors of that are modulo . Recall that for the class groups associated to or an analogous subset of does not exist.
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Mots-clés : Class groups, Dirichlet biquadratic fields
Étienne Fouvry 1 ; Peter Koymans 2

@article{JTNB_2022__34_3_637_0, author = {\'Etienne Fouvry and Peter Koymans}, title = {On {Dirichlet} biquadratic fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {637--646}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {34}, number = {3}, year = {2022}, doi = {10.5802/jtnb.1220}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1220/} }
TY - JOUR AU - Étienne Fouvry AU - Peter Koymans TI - On Dirichlet biquadratic fields JO - Journal de théorie des nombres de Bordeaux PY - 2022 SP - 637 EP - 646 VL - 34 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1220/ DO - 10.5802/jtnb.1220 LA - en ID - JTNB_2022__34_3_637_0 ER -
%0 Journal Article %A Étienne Fouvry %A Peter Koymans %T On Dirichlet biquadratic fields %J Journal de théorie des nombres de Bordeaux %D 2022 %P 637-646 %V 34 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1220/ %R 10.5802/jtnb.1220 %G en %F JTNB_2022__34_3_637_0
Étienne Fouvry; Peter Koymans. On Dirichlet biquadratic fields. Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 3, pp. 637-646. doi : 10.5802/jtnb.1220. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1220/
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