  Using high-resolution numerical simulations, we investigate mass- and
luminosity-normalized specific frequencies (T_N and S_N, respectively) of
globular cluster systems (GCSs) in order to understand the origin of the
observed U-shaped relation between S_N and V-band magnitude (M_V) of their host
galaxies.
  We adopt a biased GC formation scenario in which GC formation is truncated in
galaxy halos that are virialized at a later redshift, z_trun. T_N is derived
for galaxies with GCs today and converted into S_N for reasonable galaxy
mass-to-light-ratios (M/L). We find that T_N depends on halo mass (M_h) in the
sense that T_N can be larger in more massive halos with M_h > 10^9 M_sun, if
z_trun is as high as 15. We however find that the dependence is too weak to
explain the observed S_N-M_V relation and the wide range of S_N in low-mass
early-type galaxies with -20.5 < M_V < -16.0 mag for a reasonable constant M/L.
The M_V-dependence of S_N for the low-mass galaxies can be well reproduced, if
the mass-to-light-ratio M_h/L_V \propto M_h^{\alpha}, where \alpha is as steep
as -1. Based on these results, we propose that the origin of the observed
U-shaped S_N-M_V relation of GCSs can be understood in terms of the bimodality
in the dependence of M_h/L_V on M_h of their host galaxies. We also suggest
that the observed large dispersionin S_N in low-mass galaxies is due partly to
the large dispersion in T_N.
