  The moments of central values of families of L-functions have recently
attracted much attention and, with the work of Keating and Snaith, there are
now precise conjectures for their limiting values. We develop a simple method
to establish lower bounds of the conjectured order of magnitude for several
such families of L-functions. As an example we work out the case of the family
of all Dirichlet L-functions to a prime modulus.
