AMERICAN JOURNAL OF MATHEMATICS, v.142, no.1, pp.139 - 176
Abstract
For real quadratic number fields, we consider the order of ideal classes of split prime ideals, P. whose norm is a fixed rational prime. We collect fundamental discriminants satisfying a trivial condition for P to be principal, and show that for a positive density of such discriminants. the cyclic subgroup of the ideal class group generated by P does not have a 2-part.