Erratum to Two-torsion in the Jacobian of hyperelliptic curves over finite

Abstract. We determine the exact dimension of the F2-vector space of Fq-rational 2-torsion points in the Jacobian of a hyperelliptic curve over Fq (q odd) in terms of the degrees of the rational factors of its discriminant, and relate this to genus theory for the corresponding function field. As a corollary, we prove the existence of a point of order> 2 in the Jacobian of certain real hyperelliptic curves. Mathematics Subject Classification (2000): 11R29, 14H40 1. Introduction. Becaus