The Initial mass function of the first stars inferred from extremely
  metal-poor stars
  We compare elemental abundance patterns of $\sim 200$ extremely metal-poor
(EMP; [Fe/H]$<-3$) stars with supernova yields of metal-free stars in order to
obtain insights into the characteristic masses of the first (Population III or
Pop III) stars in the Universe. Supernova yields are prepared with
nucleosynthesis calculations of metal-free stars with various initial masses
($M=$13, 15, 25, 40 and 100 $M_{\odot}$) and explosion energies
($E_{51}=E/10^{51}$[erg]$=0.5-60$) to include low-energy, normal-energy, and
high-energy explosions. We adopt the mixing-fallback model to take into account
possible asymmetry in the supernova explosions and the yields that best-fit the
observed abundance patterns of the EMP stars are searched by varying the model
parameters. We find that the abundance patterns of the EMP stars are
predominantly best-fitted with the supernova yields with initial masses $M<40
M_{\odot}$, and that more than than half of the stars are best fitted with the
$M=25 M_\odot$ hypernova ($E_{51}=10$) models. The results also indicate that
the majority of the primordial supernovae have ejected $10^{-2}-10^{-1}
M_\odot$ of $^{56}$Ni leaving behind a compact remnant, either a neutron star
or a black hole, with mass in a range of $\sim 1.5-5 M_{\odot}$. The results
suggest that the masses of the first stars responsible for the first
metal-enrichment are predominantly $< 40 M_{\odot}$. This implies that the
higher mass first stars were either less abundant or directly collapsing into a
blackhole without ejecting heavy elements or that a supernova explosion of a
higher-mass first star inhibits the formation of the next generation of
low-mass stars at [Fe/H]$<-3$.
