Constraints on neutrino masses from the lensing dispersion of Type Ia
  supernovae
  We investigate how accurately the total mass of neutrinos is constrained from
the magnitude dispersion of SNe Ia due to the effects of gravitational lensing.
For this purpose, we use the propagation equation of light bundles in a
realistic inhomogeneous universe and propose a sample selection for supernovae
to avoid difficulties associated with small-scale effects such as strong
lensing or shear effects. With a fitting formula for the nonlinear matter power
spectrum taking account of the effects of massive neutrinos, we find that in
our model it is possible to obtain the upper limit $\Sigma m_{\nu} \simeq
1.0[{\rm eV}]$ for future optical imaging surveys with the Wide-Field InfraRed
Survey Telescope and Large Synoptic Survey Telescope. Furthermore, we discuss
how far we need to observe SNe Ia and to what extent we have to reduce the
magnitude error except for lensing in order to realize the current tightest
limit $\Sigma m_{\nu} < 0.2[{\rm eV}]$.
