Bounds of ideal class numbers of real quadratic function fields
| dc.creator | Wang, Kunpeng | |
| dc.creator | Zhang, Xianke | |
| dc.date | 2000-04-07 | |
| dc.date.accessioned | 2026-07-07T04:34:55Z | |
| dc.date.available | 2026-07-07T04:34:55Z | |
| dc.description | The theory of continued fractions of functions $ \sqrt D $ is used to give lower bound for class numbers $h(D)$ of general real quadratic function fields $K=k(\sqrt D)$ over $k={\bf F}_q(T)$. 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,$ \mbox{}\hspace{0.1cm} then $ h(D)\geq {deg}F /{deg} P;$ \hspace{0.1cm} if $D=(SG)^2+cS, $ then $ h(D)\geq {deg}S / {deg} P; $ if $D=(A^m+a)^2+A, $ then $ h(D)\geq {deg}A / {deg} P, $ where $P$ is irreducible polynomial splitting in $K, c\in {\bf F}_q$ is any constant. In addition, six types of quadratic function fields are found to have ideal class numbers bounded and bigger than one. {\bf keywords:} quadratic function field, ideal class number, continued fractions of functions | |
| dc.identifier | https://arxiv.org/abs/math/0004190 | |
| dc.identifier | http://arxiv.org/abs/math/0004190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59092 | |
| dc.subject | Number Theory | |
| dc.title | Bounds of ideal class numbers of real quadratic function fields | |
| dc.type | text |