We propose a very precise conjecture on the asymptotics of the counting function for extensions of number fields with fixed Galois group and bounded norm of the discriminant. This sharpens a previous conjecture of the author. The conjecture is known to hold for abelian groups and a few nonabelian ones. We give a heuristic argument why the conjecture should be true. We also present some computational data for the nonsolvable groups of degree 5.
Publié le : 2004-05-14
Classification:
Galois groups,
density of extensions,
distribution of discriminants,
11R32,
11R29,
12-04
@article{1090350928,
author = {Malle, Gunter},
title = {On the Distribution of Galois Groups, II},
journal = {Experiment. Math.},
volume = {13},
number = {1},
year = {2004},
pages = { 129-136},
language = {en},
url = {http://dml.mathdoc.fr/item/1090350928}
}
Malle, Gunter. On the Distribution of Galois Groups, II. Experiment. Math., Tome 13 (2004) no. 1, pp. 129-136. http://gdmltest.u-ga.fr/item/1090350928/