Prescriptions for Correcting Ultraviolet-Based Redshifts for Luminous
  Quasars at High Redshift
  High-redshift quasars typically have their redshift determined from
rest-frame ultraviolet (UV) emission lines. However, these lines, and more
specifically the prominent C IV $\lambda 1549$ emission line, are typically
blueshifted yielding highly uncertain redshift estimates compared to redshifts
determined from rest-frame optical emission lines. We present near-infrared
spectroscopy of 18 luminous quasars at $2.15 < z < 3.70$ that allows us to
obtain reliable systemic redshifts for these sources. Together with
near-infrared spectroscopy of an archival sample of 44 quasars with comparable
luminosities and redshifts, we provide prescriptions for correcting UV-based
redshifts. Our prescriptions reduce velocity offsets with respect to the
systemic redshifts by $\sim140$ km s$^{-1}$ and reduce the uncertainty on the
UV-based redshift by $\sim25\%$ with respect to the best method currently used
for determining such values. We also find that the redshifts determined from
the Sloan Digital Sky Survey Pipeline for our sources suffer from significant
uncertainties, which cannot be easily mitigated. We discuss the potential of
our prescriptions to improve UV-based redshift corrections given a much larger
sample of high redshift quasars with near-infrared spectra.
