Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties Academic Article uri icon

abstract

  • 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 PoincarĂ© 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.

author list (cited authors)

  • Cohen, P. B.

citation count

  • 9

publication date

  • July 2005