Abstract
For K K and L L number fields, χ \chi a real-valued character on Gal ( K / L ) \operatorname {Gal} (K/L) , the Artin root number W ( χ ) W(\chi ) is ± 1 \pm 1 . We analyze the question of sign for χ \chi a degree 2 character over Q {\mathbf {Q}} induced from an abelian character on a quadratic extension.
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