Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Artin root numbers for real characters

Author: Jerry Gechter
Journal: Proc. Amer. Math. Soc. 57 (1976), 35-38
MSC: Primary 12A70
MathSciNet review: 0417129
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] J. V. Armitage, Zeta functions with a zero at $ s = \tfrac{1}{2}$, Invent. Math. 20(1973), 125-138.
  • [2] E. Artin, Zur Theorie der $ L$-Reihen mit allgemeinen Gruppencharakteren, Hamb. Abh. 8(1930), 292-306.
  • [3] J. Gechter, Gaussian sums for Artin $ L$-series, Thesis, M.I.T., Cambridge, Mass., 1974.
  • [4] A. Fröhlich, Artin root numbers and normal integral bases for quaternion fields, Invent. Math. 17 (1972), 143–166. MR 0323759,
  • [5] A. Fröhlich, Artin root numbers, conductors, and representations for generalized quaternion groups, Proc. London Math. Soc. (3) 28 (1974), 402–438. MR 0364188,
  • [6] A. Weil, Dirichlet series and automorphic forms, Lecture Notes in Math., vol. 189, Springer-Verlag, New York, 1971.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12A70

Retrieve articles in all journals with MSC: 12A70

Additional Information

Keywords: Artin root number, Gauss sum, Artin $ L$-series, normal basis
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society