Artin root numbers for real characters
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- by Jerry Gechter PDF
- Proc. Amer. Math. Soc. 57 (1976), 35-38 Request permission
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
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J. V. Armitage, Zeta functions with a zero at $s = \tfrac {1}{2}$, Invent. Math. 20(1973), 125-138.
E. Artin, Zur Theorie der $L$-Reihen mit allgemeinen Gruppencharakteren, Hamb. Abh. 8(1930), 292-306.
J. Gechter, Gaussian sums for Artin $L$-series, Thesis, M.I.T., Cambridge, Mass., 1974.
- A. Fröhlich, Artin root numbers and normal integral bases for quaternion fields, Invent. Math. 17 (1972), 143–166. MR 323759, DOI 10.1007/BF01418937
- A. Fröhlich, Artin root numbers, conductors, and representations for generalized quaternion groups, Proc. London Math. Soc. (3) 28 (1974), 402–438. MR 364188, DOI 10.1112/plms/s3-28.3.402 A. Weil, Dirichlet series and automorphic forms, Lecture Notes in Math., vol. 189, Springer-Verlag, New York, 1971.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 35-38
- MSC: Primary 12A70
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417129-0
- MathSciNet review: 0417129