  Bound and resonance states of quantum dots play a significant role in
photo-absorption processes. In this work, we analyze a cylindrical quantum dot,
its spectrum and, in particular, the behaviour of the lowest resonance state
when a magnetic field is applied along the symmetry axis of the cylinder. To
obtain the energy and width of the resonance we use the complex rotation
method. As it is expected the structure of the spectrum is strongly influenced
by the Landau levels associated to the magnetic field. We show how this
structure affects the behaviour of the resonance state and that the binding of
the resonance has a clear interpretation in terms of the Landau levels and the
probability of localization of the resonance state. The localization
probability and the fidelity of the lowest energy state allows to identify two
different physical regimes, a large field-small quantum dot radius regime and a
small field-large quantum dot radius, where the binding of the resonance is
dominated by the field strength or the potential well, respectively.
