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On Coefficients of Artin L Functions as Dirichlet Series

Published online by Cambridge University Press:  20 November 2018

Takeo Funakura
Takeo Funakura*
Affiliation:
Faculty of Liberal Arts and Science, Okayama University of Science, 1-1 Ridai-cho, Okayama, 700 Japan
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Abstract

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The paper is motivated by a result of Ankeny [1] above Dirichlet L functions in 1952. We generalize this from Dirichlet L functions to Artin L functions of relative abelian extensions, by complementing the ingenious proof of Ankeny's theorem given by Iwasaki [4]. Moreover, we characterize Dirichlet L functions in the class of all Artin L functions in terms of coefficients as Dirichlet series.

Keywords

11R42
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 50 - 54
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Ankeny, N. C., A generalization of a theorem of Suetuna on Dirichlet series, Proc. Japan Acad., 28, 389–395, (1952).Google Scholar
2. Artin, E., Collected papers, Addison-Wesley, 1965.Google Scholar
3. Frohlich, A., ed. Algebraic Number Fields, Academic Press, London, 1977.Google Scholar
4. Iwasaki, K., Simple proof of a theorem of Ankeny on Dirichlet series, Proc. Japan Acad., 28, 555–557, (1952).Google Scholar
5. Serre, J.-P., Représentations Linéaires de Groupes Finis, (deuxième édition). Hermann, Paris, 1971.Google Scholar
6. Suetuna, Z., Bemerkung uber das Produkt von L-Funktionen, Tohoku Math. J. 27, 248-257, (1926).Google Scholar