  We calculate axisymmetric oscillations of rotating neutron stars composed of
the surface fluid ocean, solid crust, and fluid core, taking account of a
dipole magnetic field as strong as $B_S\sim 10^{15}$G at the surface. The
adiabatic oscillation equations for the solid crust threaded by a dipole
magnetic field are derived in Newtonian dynamics, on the assumption that the
axis of rotation is aligned with the magnetic axis so that perturbations on the
equilibrium can be represented by series expansions in terms of spherical
harmonic functions $Y_l^m(\theta,\phi)$ with different degrees $l$ for a given
azimuthal wave number $m$ around the the magnetic axis. Although the three
component models can support a rich variety of oscillation modes, axisymmetric
($m=0$) toroidal $_{l}t_n$ and spheroidal $_ls_n$ shear waves propagating in
the solid crust are our main concerns, where $l$ and $n$ denote the harmonic
degree and the radial order of the modes, respectively. In the absence of
rotation, axisymmetric spheroidal and toroidal modes are completely decoupled,
and we consider the effects of rotation on the oscillation modes only in the
limit of slow rotation. We find that the oscillation frequencies of the
fundamental toroidal torsional modes $_{l}t_n$ in the crust are hardly affected
by the magnetic field as strong as $B_S\sim 10^{15}$G at the surface. As the
radial order $n$ of the shear modes in the crust becomes higher, however, both
spheroidal and toroidal modes become susceptible to the magnetic field and
their frequencies in general get higher with increasing $B_S$. We also find
that the surface $g$ modes and the crust/ocean interfacial modes are suppressed
by a strong magnetic field, and that there appear magnetic modes in the
presence of a strong magnetic field.
