Bounds of the Ideal Class Numbers of Real Quadratic Function Fields

The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields K=k(D) over k = F q (T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e. g., if D = F 2 * c, then h(D) degF/degP; if D = (SG)2 * cS, then h(D) degS/degP; if D = (A m * a)2 * A, then h(D) degA/degP, where P is an irreducible polynomial splitting in K, c F q . In addition, three types of quadratic function fields K are found to have ideal class numbers bigger than one.