The frequency of planets around A- and M-type stars

We still know relatively little about planet frequencies as a function of stellar mass. Theoretical planet population models are currently extended to stars more (A stars) and less massive (M stars) than the Sun. For comparison, planet statistics from observational data are particularly important. It is generally accepted that giant planets in close orbits up to periods of 10 days are very rare around all kinds of stars. In this thesis I test a hypothesis of 166 additional close-in planet candidates around A-type stars in the Kepler field. I utilize radial velocity data from the Tautenburg and Ondřejov 2m telescopes to rule out a close-in stellar companion. With a statistical analysis of all 2000 Kepler A stars, I can rule out a high frequency of this kind of planets. I find an upper limit of 0.75% on the hot Jupiter frequency around main-sequence A-type stars. In this thesis I present my analysis of 125 stars of the CARMENES M dwarf survey. I compute observational detection limits for each of the stars. From the detection limits I infer the occurrence rates with two methods. With the first method I average the number of stars around which a planet could be detected in several period-mass bins (period-mass bin method). With the second method I estimate the number of planets that could be missed due to observational biases based on the actual planet detections (missed planets method). For hot Jupiters around M dwarfs I can place an upper limit of 1.4%. For low mass planets the two methods give very different results. The results of the first method (66% for periods up to 100d) are consistent with G dwarf occurrence rates. The second method results in a much higher low mass planet frequency of 1.8 planets per star. Those higher occurrence rates are consistent with what we know from transiting surveys of planets around M dwarfs. The CARMENES survey will be able to resolve this discrepancy with 200 measurements per star of 10 randomly selected inactive targets.