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Class number one and prime-producing quadratic polynomials revisited

Open Access article
 Printed: Sep 1998
  • R. A. Mollin
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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.
MSC Classifications: 11R11, 11R09, 11R29 show english descriptions Quadratic extensions
Polynomials (irreducibility, etc.)
Class numbers, class groups, discriminants
11R11 - Quadratic extensions
11R09 - Polynomials (irreducibility, etc.)
11R29 - Class numbers, class groups, discriminants

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