On equivariant global epsilon constants for certain dihedral extensions

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.