On imaginary quadratic function fields with the ideal class group to be exponent ≤2

Abstract

A necessary condition is presented for the ideal class group of an imaginary quadratic function fieldK = k (√D) (k = F q (x), 2⫮q) to be of exponent ≤2. The condition is proved to be sufficient in some cases. An analogue of Louboutin’s result in function field case is particularly presented.