  Let (S,H) be a rational algebraic surface with an ample divisor. We compute
generating functions for the Hodge numbers of the moduli spaces of H-stable
rank 2 sheaves on S in terms of certain theta functions for indefinite lattices
that were introduced in the paper alg-geom/9612020 written jointly with Don
Zagier. If H lies in the closure of the ample cone and has self-intersection 0,
it follows that the generating functions are Jacobi forms. In particular the
generating functions for the Euler numbers have a similar transformation
behaviour under SL(2,Z) as that predicted in Vafa and Witten: A strong coupling
test of S-duality. In addition we get that also the generating functions for
the signatures can be expressed in terms of modular forms. Finally it turns out
that the generating function for the signatures is also (with respect to
another developping parameter) the generating function for the Donaldson
invariants of S evaluated on all powers of the point class. The paper is
related to the recent papers math.AG/9805003 by Yoshioka, math.AG/9805054 and
math.AG/9805055 by Qin and Li and hep-th/9802168 by Minahan, Nemeschansky, Vafa
and Warner.
