  Let K be a number field, let M be the Hilbert modular orbifold of K, and let
m(q) be the probability measure uniformly supported on the cusp cross sections
of M at height q. We generalize a method of Zagier and show that m(q)
distributes uniformly with respect to the normalized Haar measure m on M as q
tends to zero, and relate the rate by which m(q) approaches m to the Riemann
hypothesis for the Dedekind zeta function of K.
