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The fundamental unit and bounds for class numbers of real quadratic fields

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 464-01, Japan
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Although class number one problem for imaginary quadratic fields was solved in 1966 by A. Baker [3] and by H. M. Stark [25] independently, the problem for real quadratic fields remains still unsettled. However, since papers by Ankeny–Chowla–Hasse [2] and H. Hasse [9], many papers concerning this problem or giving estimate for class numbers of real quadratic fields from below have appeared. There are three methods used there, namely the first is related with quadratic diophantine equations ([2], [9], [27, 28, 29, 31], [17]), and the second is related with continued fraction expantions ([8], [4], [16], [14], [18]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 124 , December 1991 , pp. 181 - 197
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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