  The oscillation frequencies of collective excitations of a trapped
Bose-Einstein condensate, when calculated in the mean-field approximation and
in the Thomas-Fermi limit, are independent of the scattering length $a$. We
calculate the leading corrections to the frequencies from quantum fluctuations
around the mean field. The semiclassical correction is proportional to $N^{1/5}
a^{6/5}$, where $N$ is the number of atoms in the condensate. The correction is
positive semidefinite and is zero for surface modes whose eigenfunctions have a
vanishing laplacian. The shift in the frequency of the lowest quadrupole mode
for an axially symmetric trap is large enough that it should be measurable in
future experiments.
