  Using cosmological hydrodynamic simulations we measure the mean transmitted
flux in the Lyman alpha forest for quasar sightlines that pass near a
foreground quasar. We find that the trend of absorption with pixel-quasar
separation distance can be fitted using a simple power law form including the
usual correlation function parameters r_{0} and \gamma so that (<F(r)> = \sum
exp(-tau_eff*(1+(r/r_{0})^(-\gamma)))). From the simulations we find the
relation between r_{0} and quasar mass and formulate this as a way to estimate
quasar host dark matter halo masses, quantifying uncertainties due to
cosmological and IGM parameters, and redshift errors. With this method, we
examine data for ~3000 quasars from the Sloan Digital Sky Survey (SDSS) Data
Release 3, assuming that the effect of ionizing radiation from quasars (the
so-called transverse proximity effect) is unimportant (no evidence for it is
seen in the data.) We find that the best fit host halo mass for SDSS quasars
with mean redshift z=3 and absolute G band magnitude -27.5 is log10(M/M_sun) =
12.48^{+0.53}_{-0.89}. We also use the Lyman-Break Galaxy (LBG) and Lyman alpha
forest data of Adelberger et al in a similar fashion to constrain the halo mass
of LBGs to be log10(M/M_sun) = 11.13^{+0.39}_{-0.55}, a factor of ~20 lower
than the bright quasars. In addition, we study the redshift distortions of the
Lyman alpha forest around quasars, using the simulations. We use the quadrupole
to monopole ratio of the quasar-Lyman alpha forest correlation function as a
measure of the squashing effect. We find that this does not have a measurable
dependence on halo mass, but may be useful for constraining cosmic geometry.
