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. We give two examples.
"Stark's conjectures and Hilbert's twelfth problem." Experiment. Math. 9 (2) 251 - 260, 2000.