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Generalized Ono invariant and Rabinovitch’s theorem for real quadratic fields

Published online by Cambridge University Press:  22 January 2016

Ryuji Sasaki
Ryuji Sasaki*
Affiliation:
Department of Mathematics, College of Science and Technology, Nihon University, Kanda, Tokyo 101, Japan
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Let d be a square-free integer. Let

and {1, ω} forms a Z-basis for the ring of integers of the quadratic field We denote by Δ and hd the discriminant and the class number of respectively.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 109 , March 1988 , pp. 117 - 124
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

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.Google Scholar
[1] Dickson, L. K., Introduction to the Theory of Numbers, Dover Publ. Inc., New York (1957).Google Scholar
[1] Hua, L. K., Introduction to Number Theory, Springer-Verlag, Berlin Heiderberg New York (1982).Google Scholar
[1] Koike, M., Ono invariant for real quadratic field, preprint.Google Scholar
[1] Kutsuna, M., On a criterion for the class number of a quadratic number field to be one, Nagoya Math. J., 79 (1980), 123–129.Google Scholar
[1] Mollin, R. A., Lower bounds for class numbers of real quadratic fields, Proc. Amer. Math. Soc, 96 (1986), 545–550.CrossRefGoogle Scholar
[1] Mollin, R. A., On the insolubility of a class of Diophantine equations and the nontriviality of the class numbers of related real quadratic fields of Richaud-Degert type, Nagoya Math. J., 105 (1987), 39–47.Google Scholar
[1] Rabinovitch, G., Eindeutig keit der Zerlegung in Primzahlfaktoren in quadratischen Zahlkorpern, J. reine angew. Math., 142 (1913), 153–164.Google Scholar
[1] Sasaki, R., On a lower bound for the class number of an imaginary quadratic field, Proc. Japan Acad., 62A (1986), 37–39.Google Scholar
[10] Sasaki, R., A characterization of certain real quadratic fields, ibid, 97–100.Google Scholar
[11] Yokoi, H., On the Diophantine equation x2—py2=±4q and the class number of real subfields of a cyclotomic field, Nagoya Math. J., 91 (1983), 151–161.Google Scholar
[12] Yokoi, H., Class number one problem for certain kind of real quadratic fields, preprint.Google Scholar