Equidistribution of Hecke eigenforms on the Hilbert modular varieties Original Research Article

Let F be a totally real number field with ring of integers image and let image be the Hilbert modular group. Given the orthonormal basis of Hecke eigenforms in S2k(Γ), one can associate a probability measure dμk on the Hilbert modular variety image. We prove that dμk tends to the invariant measure on image weakly as k→∞. This generalizes Luoʹs result [W. Luo, Equidistribution of Hecke eigenforms on the modular surface, Proc. Amer. Math. Soc. 131 (2003) 21–27] for the case F=Q.