  We present an extraction of the lowest three moments of the proton
longitudinal structure function F_L from world data between Q^2 = 0.75 and 45
(GeV/c)^2. The availability of new F_L data at low Bjorken x from HERA and at
large x from Jefferson Lab allows the first determination of these moments over
a large Q^2 range, relatively free from uncertainties associated with
extrapolations into unmeasured regions. The moments are found to be
underestimated by leading twist structure function parameterizations,
especially for the higher moments, suggesting either the presence of
significant higher twist effects in F_L and/or a larger gluon distribution at
high x.
