Equidistribution of Hecke eigenforms on the Hilbert modular varieties

Let F be a totally real number field with ring of integers O, and let Gamma = SL(2, O) be the Hilbert modular group. Given the orthonormal basis of Hecke eigenforms in S-2k (Gamma), one can associate a probability measure d mu(k) on the Hilbert modular variety Gamma\H-n. We prove that d mu(k) tends to the invariant measure on Gamma\H-n weakly as k ->infinity. This generalizes Luo's result [W. Luo, Equidistribution of Hecke eigenforms on the modular surface, Proc. Amer. Math. Soc. 131 (2003) 21-27] for the case F = Q. (C) 2007 Elsevier Inc. All rights reserved.