Quadratic Function Fields with Exponent Two Ideal Class Group
arXiv:math/0504581
Abstract
It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields that allow us to find a full list of all such field extensions for future reference. In doing so we correct some errors in earlier published literature.
To appear in the Journal of Number Theory