  Inspired by the multiplicative nature of the Ramanujan modular discriminant,
Delta, we consider physical realizations of certain multiplicative products
over the Dedekind eta-function in two parallel directions: the generating
function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces
associated to congruence subgroups of the modular group. We show that they are,
after string duality to type II, the same K3 surfaces admitting Nikulin
automorphisms. In due course, we will present some identities arising from
q-expansions as well as relations to the sporadic Mathieu group M24.
