Computation of Stark-Tamagawa units

Let be a totally real number field and let denote an odd prime number. We design an algorithm which computes strong numerical evidence for the validity of the ``Equivariant Tamagawa Number Conjecture' for the -equivariant motive , where is a cyclic extension of degree and group . This conjecture is a very deep refinement of the classical analytic class number formula. In the course of the algorithm, we compute a set of special units which must be considered as a generalization of the (conjecturally existing) Stark units associated to first order vanishing Dirichlet -functions.