Dans cette Note, nous donnons un contre-exemple à une conjecture de Malle, qui prédit le comportement asymptotique du nombre de corps de clôture galoisienne fixée et discriminant borné.
In this Note we give a counter example to a conjecture of Malle which predicts the asymptotic behavior of the counting functions for field extensions with given Galois group and bounded discriminant.
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@article{CRMATH_2005__340_6_411_0, author = {Kl\"uners, J\"urgen}, title = {A counter example to {Malle's} conjecture on the asymptotics of discriminants}, journal = {Comptes Rendus. Math\'ematique}, pages = {411--414}, publisher = {Elsevier}, volume = {340}, number = {6}, year = {2005}, doi = {10.1016/j.crma.2005.02.010}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.02.010/} }
TY - JOUR AU - Klüners, Jürgen TI - A counter example to Malle's conjecture on the asymptotics of discriminants JO - Comptes Rendus. Mathématique PY - 2005 SP - 411 EP - 414 VL - 340 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.02.010/ DO - 10.1016/j.crma.2005.02.010 LA - en ID - CRMATH_2005__340_6_411_0 ER -
%0 Journal Article %A Klüners, Jürgen %T A counter example to Malle's conjecture on the asymptotics of discriminants %J Comptes Rendus. Mathématique %D 2005 %P 411-414 %V 340 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.02.010/ %R 10.1016/j.crma.2005.02.010 %G en %F CRMATH_2005__340_6_411_0
Klüners, Jürgen. A counter example to Malle's conjecture on the asymptotics of discriminants. Comptes Rendus. Mathématique, Tome 340 (2005) no. 6, pp. 411-414. doi : 10.1016/j.crma.2005.02.010. http://archive.numdam.org/articles/10.1016/j.crma.2005.02.010/
[1] K. Belabas, Paramétrisation de structures algébriques et densité de discriminants [d'après Bhargava], Séminaire Bourbaki, 56ème année (935), 2004
[2] A survey of discriminant counting, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Computer Science, vol. 2369, Springer, Berlin, 2002, pp. 80-94
[3] On the density of discriminants of cubic fields. II, Proc. Roy. Soc. London Ser. A, Volume 322 (1971) no. 1551, pp. 405-420
[4] The number of extensions of a number field with fixed degree and bounded discriminant (2003) | arXiv
[5] Counting extensions of function fields with bounded discriminant and specified Galois group, Geometric Methods in Algebra and Number Theory, Progr. Math., vol. 235, Birkhäuser, 2005, pp. 151-168
[6] Counting nilpotent Galois extensions, J. Reine Angew. Math., Volume 572 (2004), pp. 1-26
[7] On the distribution of Galois groups, J. Numer. Theory, Volume 92 (2002), pp. 315-322
[8] On the distribution of Galois groups II, Exp. Math., Volume 13 (2004), pp. 129-135
[9] Distribution of discriminants of Abelian extensions, Proc. London Math. Soc., Volume 58 (1989), pp. 17-50
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