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Let Fq be the finite field with q elements, (26 |q), k = Fq(x), K = k( √ D) where D = D(x) = A(x)2 + a is a square-free polynomial in Fq[x] with deg A(x) ≥ 1 and a ∈ F∗q . In this paper several equivalent conditions for the ideal class number h(OK) to be one are presented and all such quadratic function fields with h(OK) = 1 are determined.

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