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Proceedings of the American Mathematical Society

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Artin root numbers for real characters


Author: Jerry Gechter
Journal: Proc. Amer. Math. Soc. 57 (1976), 35-38
MSC: Primary 12A70
MathSciNet review: 0417129
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Abstract: For $ K$ and $ L$ number fields, $ \chi $ a real-valued character on $ \operatorname{Gal} (K/L)$, the Artin root number $ W(\chi )$ is $ \pm 1$. We analyze the question of sign for $ \chi $ a degree 2 character over $ {\mathbf{Q}}$ induced from an abelian character on a quadratic extension.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0417129-0
Keywords: Artin root number, Gauss sum, Artin $ L$-series, normal basis
Article copyright: © Copyright 1976 American Mathematical Society