  We investigate the roles of magnetic fields and ambipolar diffusion during
prestellar core formation in turbulent giant molecular clouds (GMCs), using
three-dimensional numerical simulations. Our simulations focus on the shocked
layer produced by a converging flow within a GMC, and survey varying ionization
and angle between the upstream flow and magnetic field. We also include ideal
magnetohydrodynamic (MHD) and hydrodynamic models. From our simulations, we
identify hundreds of self-gravitating cores that form within 1 Myr, with masses
M ~ 0.04 - 2.5 solar-mass and sizes L ~ 0.015 - 0.07 pc, consistent with
observations of the peak of the core mass function (CMF). Median values are M =
0.47 solar-mass and L = 0.03 pc. Core masses and sizes do not depend on either
the ionization or upstream magnetic field direction. In contrast, the
mass-to-magnetic flux ratio does increase with lower ionization, from twice to
four times the critical value. The higher mass-to-flux ratio for low ionization
is the result of enhanced transient ambipolar diffusion when the shocked layer
first forms. However, ambipolar diffusion is not necessary to form low-mass
supercritical cores. For ideal MHD, we find similar masses to other cases.
These masses are 1 - 2 orders of magnitude lower than the value that defines a
magnetically supercritical sphere under post-shock ambient conditions. This
discrepancy is the result of anisotropic contraction along field lines, which
is clearly evident in both ideal MHD and diffusive simulations. We interpret
our numerical findings using a simple scaling argument which suggests that
gravitationally critical core masses will depend on the sound speed and mean
turbulent pressure in a cloud, regardless of magnetic effects.
