  Two-particle number and transverse momentum differential correlation
functions are powerful tools for unveiling the detailed dynamics and particle
production mechanisms involved in relativistic heavy-ion collisions.
Measurements of transverse momentum correlators $P_2$ and $G_2$, in particular,
provide added information not readily accessible with better known number
correlation functions $R_2$. However, it is found that the $R_2$ and $G_2$
correlators are somewhat sensitive to the details of the experimental procedure
used to measure them. They exhibit, in particular, a dependence on the
collision centrality bin width, which may have a rather detrimental impact on
their physical interpretation. A technique to correct these correlators for
collision centrality bin-width averaging is presented. The technique is based
on the hypothesis that the shape of single- and pair- probability densities
vary slower with collision centrality than the corresponding integrated yields.
The technique is tested with Pb-Pb simulations based on the HIJING and
ultrarelativistic quantum molecular dynamics models and shown to enable a
precision better than 1% for particles in the kinematic range $0.2 \leq p_{\rm
T} \leq 2.0$ GeV/$c$.
