Computing the Hilbert Class Field of Real Quadratic Fields

Henri Cohen (1) , Xavier-François Roblot (1)

1 A2X - Théorie des Nombres et Algorithmique Arithmétique

Using the units appearing in Stark's conjectures on the values of L-functions at s=0, we give a complete algorithm for computing an explicit generator of the Hilbert class field of a real quadratic field.

Domaines: Théorie des nombres [math.NT]

Henri Cohen, Xavier-François Roblot. Computing the Hilbert Class Field of Real Quadratic Fields. Mathematics of Computation, 2000, 69 (231), pp.1229-1244. ⟨hal-00863026⟩