Hyperbolic distribution problems on Siegel 3-folds and Hilbert modular varieties

摘要

We generalize to Hilbert modular varieties of arbitrary dimension the work ofW. Duke (Inventiones 1988) on the equidistribution of Heegner points and ofprimitive positively oriented closed geodesics in the Poincare upper halfplane, subject to certain subconvexity results. We also prove vanishing resultsfor limits of cuspidal Weyl sums associated with analogous problems for theSiegel upper half space of degree 2. In particular, these Weyl sums areassociated with families of Humbert surfaces in Siegel 3-folds and of modularcurves in these Humbert surfaces.