We generalize to Hilbert modular varieties of arbitrary dimension
the work of W. Duke [16] on the equidistribution of Heegner
points and of primitive positively oriented closed geodesics in
the Poincaré upper half-plane, subject to certain subconvexity
results. We also prove vanishing results for limits of cuspidal
Weyl sums associated with analogous problems for the Siegel upper
half-space of degree 2. In particular, these Weyl sums are
associated with families of Humbert surfaces in Siegel 3-folds and
of modular curves in these Humbert surfaces.