On -Weierstrass sets and gaps

Let X be a nonsingular projective curve of genus g 1 defined over a field which is assumed to be the full field of constants of , and let be a linear system of divisors on X. We define the set of -Weierstrass gaps at the rational points P1,…,Pn of X as being formed by the n-tuples α=(α1,…,αn) such that for some j {1,…,n} (here and ). We call the -Weierstrass set associated to and P1,…Pn. The main result of this paper proves a sharp lower bound for .