Bounds of the Ideal Class Numbers of Real Quadratic Function Fields
KunPengWANG, XianKeZHANG · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2004
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=Fq(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∈Fq．In addition，three types of quadratic function fields K are found to have ideal class numbers bigger than one．