An Extended Zel'dovich Model for the Halo Mass Function
  A new way to construct a fitting formula for the halo mass function is
presented. Our formula is expressed as a solution to the modified Jedamzik
matrix equation that automatically satisfies the normalization constraint. The
characteristic parameters expressed in terms of the linear shear eigenvalues
are empirically determined by fitting the analytic formula to the numerical
results from the high-resolution N-body simulation and found to be independent
of scale, redshift and background cosmology. Our fitting formula with the
best-fit parameters is shown to work excellently in the wide mass-range at
various redshifts: The ratio of the analytic formula to the N-body results
departs from unity by up to 10% and 5% over 10^{11}<= M/(M_sun/h)<= 5x10^{15}
at z=0,\ 0.5 and 1 for the FoF-halo and SO-halo cases, respectively.
