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On Real Quadratic Fields Containing Units with Norm -1

Published online by Cambridge University Press:  22 January 2016

Hideo Yokoi
Hideo Yokoi*
Affiliation:
Mathematical Institute, Nagoya University
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Let Q be the rational number field, and let K = (D > 0 a rational integer) be a real quadratic field. Then, throughout this paper, we shall understand by the fundamental unit εD of the normalized fundamental unit εD > 1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 33 , November 1968 , pp. 139 - 152
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Ankeny, N.C., Chowla, S. and Hasse, H., On the class number of the real subfield of a cyclotomic field. J. reine angew. Math. 217 (1965), 217–220.CrossRefGoogle Scholar
[2] Degert, G., Über die Bestimmung der Grundeinheit gewisser reell-quadratischer Zahlkörper. Abh. math. Sem. Univ. Hamburg 22 (1958), 92–97.CrossRefGoogle Scholar
[3] Hasse, H., Über mehrklassige, aber eingeschlechtige reell-quadratische Zahlkörper. Elemente der Mathematik 20 (1965), 49–59.Google Scholar
[4] Nagell, T., Bemerkung über die Klassenzahl reell-quadratischer Zahlkörper. Det Kongelige Norske Videnskabens Selskab, Forhandlinger 11 (1938), 7–10.Google Scholar
[5] Rédei, L., Über die Pellsche Gleichung t2–du2 = –1. J. reine angew. Math. 173 (1935), 193–221.CrossRefGoogle Scholar
[6] Richaud, C., Sur la résolution des équations x2 – Ay2 = ± 1. Atti Accad. pontif. Nuovi Lincei (1866), 177–182.Google Scholar