On the existence of non-special divisors of degree $g$ and $g-1$ in algebraic function fields over $\F_q$
| dc.creator | Ballet, Stephane | |
| dc.creator | Brigand, Dominique Le | |
| dc.date | 2004-10-06 | |
| dc.date | 2004-10-13 | |
| dc.date.accessioned | 2026-07-07T05:13:02Z | |
| dc.date.available | 2026-07-07T05:13:02Z | |
| dc.description | We study the existence of non-special divisors of degree $g$ and $g-1$ for algebraic function fields of genus $g\geq 1$ defined over a finite field $\F_q$. In particular, we prove that there always exists an effective non-special divisor of degree $g\geq 2$ if $q\geq 3$ and that there always exists a non-special divisor of degree $g-1\geq 1$ if $q\geq 4$. We use our results to improve upper and upper asymptotic bounds on the bilinear complexity of the multiplication in any extension $\F_{q^n}$ of $\F_q$, when $q=2^r\geq 16$. | |
| dc.description | 21 pages: added Remark 22 at the end of the paper | |
| dc.identifier | https://arxiv.org/abs/math/0410193 | |
| dc.identifier | http://arxiv.org/abs/math/0410193 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72798 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11R58 | |
| dc.title | On the existence of non-special divisors of degree $g$ and $g-1$ in algebraic function fields over $\F_q$ | |
| dc.type | text |