  For a hard-core Bose gas on a one-dimensional lattice we find characteristic
oscillations in the density-density correlation function. Their wavelength
diverges as the system undergoes a continuous transition from an incommensurate
to a Mott insulating phase. The associated static structure factor vanishes as
the Mott insulating phase is approached. The qualitative picture is unchanged
when a weak confinig potential is applied to the system.
