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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The Brumer-Stark conjecture in some families of extensions of specified degree


Authors: Cornelius Greither, Xavier-François Roblot and Brett A. Tangedal
Journal: Math. Comp. 73 (2004), 297-315
MSC (2000): Primary 11R42; Secondary 11R29, 11R80, 11Y40
Published electronically: June 19, 2003
Corrigendum: Math. Comp. 84 (2015), 955--957
MathSciNet review: 2034123
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Abstract: As a starting point, an important link is established between Brumer's conjecture and the Brumer-Stark conjecture which allows one to translate recent progress on the former into new results on the latter. For example, if $K/F$ is an abelian extension of relative degree $2p$, $p$ an odd prime, we prove the $l$-part of the Brumer-Stark conjecture for all odd primes $l\ne p$ with $F$ belonging to a wide class of base fields. In the same setting, we study the $2$-part and $p$-part of Brumer-Stark with no special restriction on $F$ and are left with only two well-defined specific classes of extensions that elude proof. Extensive computations were carried out within these two classes and a complete numerical proof of the Brumer-Stark conjecture was obtained in all cases.


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Additional Information

Cornelius Greither
Affiliation: Institut für theoretische Informatik und Mathematik, Fakultät für Informatik, Universität der Bundeswehr München, 85577 Neubiberg, F. R. Germany
Email: greither@informatik.unibw-muenchen.de

Xavier-François Roblot
Affiliation: Institut Girard Desargues, Université Claude Bernard (Lyon I), 69622 Villeurbanne, France
Email: roblot@euler.univ-lyon1.fr

Brett A. Tangedal
Affiliation: Department of Mathematics, College of Charleston, Charleston, South Carolina 29424-0001
Email: tangedalb@cofc.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01565-5
PII: S 0025-5718(03)01565-5
Keywords: Algebraic number fields, Brumer-Stark conjecture
Received by editor(s): December 20, 2001
Published electronically: June 19, 2003
Article copyright: © Copyright 2003 American Mathematical Society