On the Computation of All Extensions of a p-Adic Field of a Given Degree

Sebastian Pauli (1) , Xavier-François Roblot (2)

1 CICMA - Centre interuniversitaire en calcul mathématique algébrique [Montréal]
2 IGD - Institut Girard Desargues

Let k be a p-adic field. It is well-known that k has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of k of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all these extensions.

Domaines: Théorie des nombres [math.NT]

Sebastian Pauli, Xavier-François Roblot. On the Computation of All Extensions of a p-Adic Field of a Given Degree. Mathematics of Computation, 2001, 70 (236), pp.1641-1659. ⟨hal-00863052⟩