  We present the results that are necessary in the ongoing lattice calculations
of the gluon parton distribution functions (PDFs) within the pseudo-PDF
approach. We identify the two-gluon correlator functions that contain the
invariant amplitude determining the gluon PDF in the light-cone $z^2 \to 0$
limit, and perform one-loop calculations in the coordinate representation in an
explicitly gauge-invariant form. Ultraviolet (UV) terms, which contain $\ln
(-z^2)$-dependence cancel in the reduced Ioffe-time distribution (ITD), and we
obtain the matching relation between the reduced ITD and the light-cone ITD.
Using a kernel form, we get a direct connection between lattice data for the
reduced ITD and the normalized gluon PDF.
