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Imaginary bicyclic biquadratic fields with the real quadratic subfield of class-number one

Published online by Cambridge University Press:  22 January 2016

Hideo Yokoi
Hideo Yokoi*
Affiliation:
Department of Mathematics, College of General Education, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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It has been proved by A. Baker [1] and H. M. Stark [7] that there exist exactly 9 imaginary quadratic fields of class-number one. On the other hand, G.F. Gauss has conjectured that there exist infinitely many real quadratic fields of class-number one, and the conjecture is now still unsolved.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 102 , June 1986 , pp. 91 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

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[10] Yokoi, H., On the class number of a relatively cyclic number field, Nagoya Math. J., 29 (1967), 31–44.Google Scholar