Abstract
Let K be an imaginary abelian number field. We determine the unit index of K of certain type whose conductor is a product of two or three prime powers. As a consequence we construct some counterexamples to Satz 29 in Hasse's monograph [2].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hasse, H.: Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, la und II, Physica-Verlag, Würzburg-Wien, 1965
Hasse, H.: über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952 (reproduction: Springer-Verlag, Berlin, 1985)
Hirabayashi, M. and Yoshino, K.: The Unit Indices of Imaginary Abelian Number Fields, Proc. Japan Acad.60 Ser. A, 215–217 (1984)
Hirabayashi, M. and Yoshino, K.: On the Relative Class Number of the Imaginary Abelian Number Field I and II, Memoirs of the College of Liberal Arts and Kanazawa Medical University, vol.9, 5–53 (1981) and vol.10, 33–81 (1982)
Iwasawa, K.: A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg20, 257–258 (1956)
Washington, L. C.: Introduction to Cyclotomic Fields, Springer-Verlag, New York, 1982
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hirabayashi, M., Yoshino, Ki. Remarks on unit indices of imaginary abelian number fields. Manuscripta Math 60, 423–436 (1988). https://doi.org/10.1007/BF01258662
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01258662