  We generalize to Hilbert modular varieties of arbitrary dimension the work of
W. Duke (Inventiones 1988) on the equidistribution of Heegner points and of
primitive positively oriented closed geodesics in the Poincare 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.
