Class number one and prime-producing quadratic polynomials revisited

http://dx.doi.org/10.4153/CMB-1998-045-6
Canad. Math. Bull. 41(1998), 328-334

  Published:1998-09-01
 Printed: Sep 1998

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.