Quadratic function fields with exponent two ideal class group

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.