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Article electronically published on May 30, 2003 COMPUTATION OF STARK-TAMAGAWA UNITS

By W. Bley


Abstract. Let K be a totally real number field and let l 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 Q[G]-equivariant motive h0 (Spec(L)), where L/K is a cyclic extension of degree l and group G. 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 L-functions. 1

Year: 2011
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