  We give a dimension formula for the space of logarithm-free series solutions
to an A-hypergeometric (or a GKZ hypergeometric) system. In the case where the
convex hull spanned by A is a simplex, we give a rank formula for the system,
characterize the exceptional set, and prove the equivalence of the
Cohen-Macaulayness of the toric variety defined by A with the emptiness of the
exceptional set. Furthermore we classify A-hypergeometric systems as analytic
D-modules.
