SÉMINAIRE DE THÉORIE DES NOMBRES 2004-2005 Le Vendredi à 15 heures 30 en Salle de Conférence Organisateur : Laurent Herr

Let $D_f$ be the discriminant of the trinomial $f(t)=t^n+at+b$, where $a,b$ runs over the set of positive integers. H. Osada showed that under certain conditions the Galois group of this trinomial is isomorphic to $S_n$. Moreover, if $K_f$ is the splitting field of $f(t)$ over $Q$, then $K_f$ is unramified at all finite primes over $Q(\sqrt D_f)$ with the alternating group $A_n$ of degree $n$ as the Galois group. In this talk , we shall discuss a quantitative version of Osada's result.