  The one-loop polarization function of graphene has been calculated at zero
temperature for arbitrary wavevector, frequency, chemical potential (doping),
and band gap. The result is expressed in terms of elementary functions and is
used to find the dispersion of the plasmon mode and the static screening within
the random phase approximation. At long wavelengths the usual square root
behaviour of plasmon spectra for two-dimensional (2D) systems is obtained. The
presence of a small (compared to a chemical potential) gap leads to the
appearance of a new undamped plasmon mode. At greater values of the gap this
mode merges with the long-wavelength one, and vanishes when the Fermi level
enters the gap. The screening of charged impurities at large distances differs
from that in gapless graphene by slower decay of Friedel oscillations ($1/r^2$
instead of $1/r^3$), similarly to conventional 2D systems.
