  The linear response of two-dimensional electron gas in a perpendicular
magnetic field in the presence of a spatially dependent classically smooth
electrostatic potential is studied theoretically, by application of the Kubo
formula for nonlocal conductivity tensor. In the classical transport regime, a
general expression for the conductivity tensor through the correlation
functions of the homogeneous electron gas is derived. The quantum transport
regime, when Landau quantization is essential, is studied for the case of
unidirectional periodic potential modulation. Apart from the Shubnikov-de Haas
oscillations, the resistivity can demonstrate quantum oscillations with larger
periods and smaller amplitudes, which survive when temperature increases. These
oscillations exist when the modulation amplitude considerably exceeds the
cyclotron energy so the Landau subbands, formed out of the Landau levels by the
modulation potential, overlap in the energy domain. Both diagonal components of
the resistivity tensor demonstrate oscillations related to modification of the
density of states by the modulation. In addition, the resistivity component
perpendicular to the modulation axis, which is caused by the
scattering-assisted hopping transport, shows another kind of oscillations
related to enhancement of the hopping probability when the guiding center of
cyclotron orbit shifts by the doubled cyclotron radius. It is suggested that
such high-temperature oscillations can be detected under conditions when the
modulation period considerably exceeds the cyclotron radius.
