On real quadratic function fields of Chowla type with ideal class number one

Let F-q be the finite field with q elements, (2 inverted iota q), k = F-q(x ), K = k(root D) where D = D(x) = A(x)(2) + a is a square-free polynomial i n F-q[x] with deg A(x) greater than or equal to 1 and a is an element of F- q*. In this paper several equivalent conditions for the ideal class number h(O-K) to be one are presented and all such quadratic function fields with h(O-K) = 1 are determined.