  The CARMENES exoplanet survey of M dwarfs has obtained more than 18 000
spectra of 329 nearby M dwarfs over the past five years as part of its
guaranteed time observations (GTO) program. We determine planet occurrence
rates with the 71 stars from the GTO program for which we have more than 50
observations. We use injection-and-retrieval experiments on the radial-velocity
(RV) time series to measure detection probabilities. We include 27 planets in
21 planetary systems in our analysis. We find 0.06+0.04-0.03 giant planets (100
M_Earth < M_pl sin i < 1000 M_Earth) per star in periods of up to 1000 d, but
due to a selection bias this number could be up to a factor of five lower in
the whole 329-star sample. The upper limit for hot Jupiters (orbital period of
less than 10 d) is 0.03 planets per star, while the occurrence rate of planets
with intermediate masses (10 M_Earth < M_pl sin i < 100 M_Earth) is
0.18+0.07-0.05 planets per star. Less massive planets with 1 M_Earth < M_pl sin
i < 10 M_Earth are very abundant, with an estimated rate of 1.32+0.33-0.31
planets per star for periods of up to 100 d. When considering only late M
dwarfs with masses M_star < 0.34 M_sol, planets more massive than 10 M_Earth
become rare. Instead, low-mass planets with periods shorter than 10 d are
significantly overabundant. For orbital periods shorter than 100 d, our results
confirm the known stellar mass dependences from the Kepler survey: M dwarfs
host fewer giant planets and at least two times more planets with M_pl sin i <
10 M_Earth than G-type stars. In contrast to previous results, planets around
our sample of very low-mass stars have a higher occurrence rate in short-period
orbits of less than 10 d. Our results demonstrate the need to take into account
host star masses in planet formation models.
