On the existence of non-special divisors of degree g and g-1 in algebraic function fields over image Original Research Article

We study the existence of non-special divisors of degree g and g-1 for algebraic function fields of genus ggreater-or-equal, slanted1 defined over a finite field image. In particular, we prove that there always exists an effective non-special divisor of degree ggreater-or-equal, slanted2 if qgreater-or-equal, slanted3 and that there always exists a non-special divisor of degree g-1greater-or-equal, slanted1 if qgreater-or-equal, slanted4. We use our results to improve upper and upper asymptotic bounds on the bilinear complexity of the multiplication in any extension image of image, when q=2rgreater-or-equal, slanted16.