  My thesis deals with a fundamental question of high energy gamma-ray
astronomy. Namely, I studied the cut-off shape of the Crab pulsar spectrum to
distinguish between the leading scenarios for the pulsar models.
  Pulsars are celestial objects, which emit periodic pulsed electromagnetic
radiation (pulsation) from radio to high energy gamma-rays. Two major scenarios
evolved in past 40 years to explain the pulsation mechanism: the inner
magnetosphere scenario and the outer magnetosphere scenario. Both scenarios
predict a high energy cut-off in the gamma-ray energy spectrum, but with
different cut-off sharpness. An exponential cut-off is expected for the outer
magnetosphere scenario while a super-exponential cut-off is predicted for the
inner magnetosphere scenario. Therefore, one of the best ways to confirm or
rule out these scenarios is to measure the energy spectrum of a pulsar at
around the cut-off energy, i.e., at energies between a few GeV and a few tens
of GeV. All past attempts (>10) to measure pulsars with ground-based
instruments have failed while satellite-borne detectors had a too small area to
study detailed spectra in the GeV domain.
  In this thesis, the gamma-ray emission at around the cut-off energy from the
Crab pulsar is studied with the MAGIC telescope. The public data of the
satellite-borne gamma-ray detector, Fermi-LAT, are also analyzed in order to
discuss the MAGIC observation results in comparison with the adjacent energy
band.
