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Computation of Stark-Tamagawa units


Author: W. Bley
Journal: Math. Comp. 72 (2003), 1963-1974
MSC (2000): Primary 11R27, 11R29, 11R42
DOI: https://doi.org/10.1090/S0025-5718-03-01561-8
Published electronically: May 30, 2003
MathSciNet review: 1986815
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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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Additional Information

W. Bley
Affiliation: Institut für Mathematik, Universität Augsburg, Universitätsstrasse 8, D-86159 Augsburg, Germany
Email: bley@math.uni-augsburg.de

DOI: https://doi.org/10.1090/S0025-5718-03-01561-8
Received by editor(s): November 7, 2001
Received by editor(s) in revised form: April 26, 2002
Published electronically: May 30, 2003
Additional Notes: The author was supported in part by a DFG Grant.
Article copyright: © Copyright 2003 American Mathematical Society

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