| Résume | Given a number field $k$ and a finite group $G$ we are interested inthe number $N(k,G,x)$ of Galois extensions of $k$ with group $G$ andnorm of the discriminant bounded by $x$. We present a conjecture onthe asymptotic behaviour of this function as $x$ tends to $\infty$ (infact even for the case of non-Galois extensions), and give some evidencefor it. We will also report on the proof of a weak form of this conjecturein the case of nilpotent groups $G$ and related results. |
