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Numerical Verification of the Brumer-Stark Conjecture

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Algorithmic Number Theory (ANTS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1838))

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Abstract

The construction of group ring elements that annihilate the ideal class groups of totally complex abelian extensions of ℚ is classical and goes back to work of Kummer and Stickelberger. A generalization to totally complex abelian extensions of totally real number fields was formulated by Brumer. Brumer’s formulation fits into a more general framework known as the Brumer-Stark conjecture. We will verify this conjecture for a large number of examples belonging to an extended class of situations where the general status of the conjecture is still unknown.

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Author information

Authors and Affiliations

  1. CICMA, Concordia University, Montréal, Québec, Canada

    Xavier-François Roblot

  2. College of Charleston, Charleston, SC, 29424, USA

    Brett A. Tangedal

Authors
  1. Xavier-François Roblot
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  2. Brett A. Tangedal
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Editor information

Editors and Affiliations

  1. Mathematisch Instituut, Universiteit Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Wieb Bosma

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© 2000 Springer-Verlag Berlin Heidelberg

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Roblot, XF., Tangedal, B.A. (2000). Numerical Verification of the Brumer-Stark Conjecture. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_32

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  • DOI: https://doi.org/10.1007/10722028_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67695-9

  • Online ISBN: 978-3-540-44994-2

  • eBook Packages: Springer Book Archive

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