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On equivariant global epsilon constants for certain dihedral extensions
Author(s):
Manuel
Breuning.
Journal:
Math. Comp.
73
(2004),
881-898.
MSC (2000):
Primary 11R33;
Secondary 11R42, 11Y40
Posted:
August 19, 2003
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Abstract:
We consider a conjecture of Bley and Burns which relates the epsilon constant of the equivariant Artin  -function of a Galois extension of number fields to certain natural algebraic invariants. For an odd prime number  , we describe an algorithm which either proves the conjecture for all degree  dihedral extensions of the rational numbers or finds a counterexample. We apply this to show the conjecture for all degree  dihedral extensions of  . 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
Email:
breuning@mth.kcl.ac.uk
DOI:
10.1090/S0025-5718-03-01605-3
PII:
S 0025-5718(03)01605-3
Keywords:
Equivariant Tamagawa number conjecture,
equivariant epsilon constants,
dihedral extensions
Received by editor(s):
November 25, 2002
Posted:
August 19, 2003
Additional Notes:
The author was supported by the DAAD and the EPSRC
Copyright of article:
Copyright
2003,
American Mathematical Society
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