  We describe a search for close spectroscopic dwarf M star binaries using data
from the Sloan Digital Sky Survey (SDSS) to address the question of the rate of
occurrence of multiplicity in M dwarfs. We use a template fitting technique to
measure radial velocities from 145,888 individual spectra obtained for a
magnitude-limited sample of 39,543 M dwarfs. Typically, the three or four
spectra observed for each star are separated in time by less than four hours,
but for ~17% of the stars, the individual observations span more than two days.
In these cases we are sensitive to large amplitude radial velocity variations
on time scales comparable to the separation between the observations. We use a
control sample of objects having observations taken within a four hour period
to make an empirical estimate of the underlying radial velocity error
distribution and simulate our detection efficiency for a wide range of binary
star systems. We find the frequency of binaries among the dwarf M stars with
a<0.4 AU to be 3-4%. Comparison with other samples of binary stars demonstrates
that the close binary fraction, like the total binary fraction, is an
increasing function of primary mass.
