Distribution of primordial black holes and 21cm signature
  We show that the number of primordial black holes (PBHs) which is originated
from primordial density perturbations with moderately-tilted power spectrum
fluctuates following the log-normal distribution, while it follows the Poisson
distribution if the spectrum is steeply blue. The log-normal, as well as the
Poisson, fluctuation of the PBH number behaves as an isocurvature mode and
affects the matter power spectrum and the halo mass function in a different way
from those for the Poisson case. The future 21cm observation can potentially
put a stronger constraint on the PBH fraction than the current one in a wide
mass range, $10^{-5}M_\odot$--$10M_\odot$.
