On the existence of non-special divisors of degree g and in algebraic function fields over

✍ Scribed by S. Ballet; D. Le Brigand

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 211 KB
• Volume: 116
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2005.04.009

✦ Synopsis

We study the existence of non-special divisors of degree g and g -1 for algebraic function fields of genus g 1 defined over a finite field F q . In particular, we prove that there always exists an effective non-special divisor of degree g 2 if q 3 and that there always exists a non-special divisor of degree g -1 1 if q 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 16.