Computation of Stark-Tamagawa units

Bley, W.

doi:10.1090/S0025-5718-03-01561-8

Computation of Stark-Tamagawa units
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by W. Bley PDF

Math. Comp. 72 (2003), 1963-1974 Request permission

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 ${\mathbb {Q}[G]}$-equivariant motive $h^0(\mathrm {Spec}(L))$, 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.

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