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

We generalize to Hilbert modular varieties of arbitrary dimension the work of W. Duke on the equidistribution of Heegner points and of primitive positively oriented closed geodesics in the Poincar upper half-plane, subject to certain sub-convexity 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.

Overview