Stark's Conjectures and Hilbert's Twelfth Problem

Xavier-François Roblot (1)

1 A2X - Théorie des Nombres et Algorithmique Arithmétique

We give a constructive proof of a theorem of Tate, which states that (under Stark's Conjecture) the field generated over a totally real field K by the Stark units contains the maximal real abelian extension of K. As a direct application of this proof, we show how one can compute explicitly real abelian extensions of K.

Domaines: Théorie des nombres [math.NT]

Xavier-François Roblot. Stark's Conjectures and Hilbert's Twelfth Problem. Experimental Mathematics, 1999, 9 (2), pp.251-260. ⟨hal-00863014⟩