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On equivariant global epsilon constants for certain dihedral extensions

Author: Manuel Breuning
Journal: Math. Comp. 73 (2004), 881-898
MSC (2000): Primary 11R33; Secondary 11R42, 11Y40
Published electronically: August 19, 2003
MathSciNet review: 2031413
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a conjecture of Bley and Burns which relates the epsilon constant of the equivariant Artin $L$-function of a Galois extension of number fields to certain natural algebraic invariants. For an odd prime number $p$, we describe an algorithm which either proves the conjecture for all degree $2p$ dihedral extensions of the rational numbers or finds a counterexample. We apply this to show the conjecture for all degree $6$dihedral extensions of $\mathbb Q$. The correctness of the algorithm follows from a finiteness property of the conjecture which we prove in full generality.

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Additional Information

Manuel Breuning
Affiliation: Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom

Keywords: Equivariant Tamagawa number conjecture, equivariant epsilon constants, dihedral extensions
Received by editor(s): November 25, 2002
Published electronically: August 19, 2003
Additional Notes: The author was supported by the DAAD and the EPSRC
Article copyright: © Copyright 2003 American Mathematical Society