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On prime valued polynomials and class numbers of real quadratic fields

Published online by Cambridge University Press:  22 January 2016

R.A. Mollin  and
H.C. Williams
R.A. Mollin
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4
H.C. Williams
Affiliation:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada, RST 2N2
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Gauss conjectured that there are infinitely many real quadratic fields with class number one. Today this is still an open problem. Moreover, as Dorian Goldfeld, one of the recipients of the 1987 Cole prize in number theory (for his work on another problem going back to Gauss) recently stated in his acceptance of the award: “This problem appears quite intractible at the moment.” However there has recently been a search for conditions which are tantamount to class number one for real quadratic fields. This may be viewed as an effort to shift the focus of the problem in order to understand more clearly the inherent difficulties, and to reveal some other beautiful interrelationships.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 112 , December 1988 , pp. 143 - 151
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

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