Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T21:09:22.395Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Analytic Determination of the Trace Form

Published online by Cambridge University Press:  20 November 2018

Robert Perlis
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Dedekind zeta function of an algebraic number field E determines the rational equivalence class of the trace form of E. The Hasse symbols of the trace form are related to the local Artin root numbers of the zeta function by formulas of Serre and Deligne. This is used to settle the question of which families of complex numbers appear as the local Artin root numbers of a continuous real representation of the absolute Galois group of ℚ.

Keywords

10C02
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 422 - 430
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Conner, P.E. and Pedis, R., A Survey of Trace Forms of Algebraic Number Fields, World Scientific Publishing Company, Singapore (1984).Google Scholar
2. Curtis, M., Matrix Groups, Springer-Verlag, New York (1979).Google Scholar
3. Deligne, P., Les constantes locales de l'équation fonctionnelle de la fonction L d'Artin d'une représentation orthogonale, Inv. Math. 35 (1976), pp. 296–316.Google Scholar
4. Fröhlich, A., Orthogonal representations of Galois groups, Stiefel—Whitney classes, and Hasse—Witt invariants, preprint (1984), p. 1—60.Google Scholar
5. Marcus, M. and Mine, H., Introduction to Linear Algebra, Macmillan, New York (1965).Google Scholar
6. Martinet, J., Character theory and Artin L-functions, in Algebraic Number Fields, Academic Press, New York (1977), pp. 1–87.Google Scholar
7. Perlis, R., On the equation ζK(s) = ζ,K'(s), J. Number Theory 9 (1977), pp. 342–360.Google Scholar
8. Serre, J.-P., L'invariant de Witt de la forme Tr(x2), Commentarii Mathematici Helvetici 59 (1984), pp. 651–676.Google Scholar
9. Tate, J., Local Constants, in Algebraic Number Fields, Academic Press, New York (1977), pp. 89–131.Google Scholar
10. Taussky-Todd, O., The discriminant matrices of an algebraic number field, J. London Math. Soc, 43 (1968), pp. 152–154.Google Scholar