Counting discriminants of number fields

Cohen, Henri; Diaz y Diaz, Francisco; Olivier, Michel

Journal de théorie des nombres de Bordeaux, Tome 18 (2006) no. 3, pp. 573-593.

Pour tout groupe de permutations transitif sur $n$ lettres $G$ avec $n\le 4$ nous donnons sans démonstration des résultats, des conjectures et des calculs numériques sur le nombre de discriminants de corps de nombres $L$ de degré $n$ sur $\mathbb{Q}$ tels que le groupe de Galois de la clôture galoisienne de $L$ soit isomorphe à $G$.

For each transitive permutation group $G$ on $n$ letters with $n\le 4$, we give without proof results, conjectures, and numerical computations on discriminants of number fields $L$ of degree $n$ over $\mathbb{Q}$ such that the Galois group of the Galois closure of $L$ is isomorphic to $G$.

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