  Let F be a totally real number field, and let f traverse a sequence of
non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n),
trivial central character and full level. We show that the mass of f
equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to
infinity.
  Our result answers affirmatively a natural analogue of a conjecture of
Rudnick and Sarnak (1994). Our proof generalizes the argument of
Holowinsky-Soundararajan (2008) who established the case F = Q. The essential
difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of
the equidistribution problem in terms of manageable shifted convolution sums of
Fourier coefficients to the case of a number field with nontrivial unit group.

Number Theory