  Comparisons between the planet populations around solar-type stars and those
orbiting M dwarfs shed light on the possible dependence of planet formation and
evolution on stellar mass. However, such analyses must control for other
factors, i.e. metallicity, a stellar parameter which strongly influences the
occurrence of gas giant planets. We obtained infrared spectra of 121 M dwarfs
stars monitored by the California Planet Search (CPS) and determined
metallicities with an accuracy of 0.08 dex. The mean and standard deviation of
the sample is -0.05 and 0.20 dex, respectively. We parameterized the
metallicity dependence of the occurrence of giant planets on orbits with period
less than 2 yr around solar-type stars and applied this to our M dwarf sample
to estimate the expected number of giant planets. The number of detected
planets (3) is lower than the predicted number (6.4) but the difference is not
very significant (12% probability of finding as many or fewer planets). The
three M dwarf planet hosts are not especially metal rich and the most likely
value of the power-law index relating planet occurrence to metallicity is 1.06
dex per dex for M dwarfs compared to 1.80 for solar-type stars; this
difference, however, is comparable to uncertainties. Giant planet occurrence
around both types of stars allows, but does not necessarily require, mass
dependence of $\sim 1$ dex per dex. The actual planet-mass-metallicity relation
may be complex and elucidating it will require larger surveys like those to be
conducted by ground-based infrared spectrographs and the Gaia space astrometry
mission.
