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On Prime Discriminants

Published online by Cambridge University Press:  22 January 2016

Larry Joel Goldstein
Larry Joel Goldstein*
Affiliation:
Department of Mathematics University of MarylandCollege Park, Maryland 20742
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Let be a quadratic field of discriminant d. We say that d is a prime discriminant if d is divisible by exactly one rational prime. It is classically known that the prime discriminants are given by

(p an odd prime).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 45 , February 1972 , pp. 119 - 127
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Furuta, Y. “The Genus Field and Genus Number in Algebraic Number Fields,” Nagoya Math. J. 29 (1967), pp. 281–285.CrossRefGoogle Scholar
[2] Siegel, C.L. Lectures on Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1961.Google Scholar