On equivariant global epsilon constants for certain dihedral extensions

Breuning, Manuel

doi:10.1090/S0025-5718-03-01605-3

On equivariant global epsilon constants for certain dihedral extensions
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by Manuel Breuning;

Math. Comp. 73 (2004), 881-898

DOI: https://doi.org/10.1090/S0025-5718-03-01605-3

Published electronically: 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 $L$-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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