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Class Number One and Prime-Producing Quadratic Polynomials Revisited

Published online by Cambridge University Press:  20 November 2018

R. A. Mollin
R. A. Mollin*
Affiliation:
Department of Mathematics and Statistics University of Calgary Calgary, Alberta T2N 1N4, e-mail: ramollin@math.ucalgary.ca Website: http://www.math.ucalgary.ca/∼ramollin/
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Abstract

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Over a decade ago, this author produced class number one criteria for real quadratic fields in terms of prime-producing quadratic polynomials. The purpose of this article is to revisit the problem from a new perspective with new criteria. We look at the more general situation involving arbitrary real quadratic orders rather than the more restrictive field case, and use the interplay between the various orders to provide not only more general results, but also simpler proofs.

Keywords

11R1111R0911R29
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 328 - 334
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Mollin, R. A., Quadratics. CRC Press, Boca Raton, New York, London, Tokyo, 1995.Google Scholar
2. Weinberger, P., Real quadratic fieldswith class groups divisible by n. J.Number Theory 5 (1973), 237–241.Google Scholar