  The STAR Collaboration reports measurements of the longitudinal double-spin
asymmetry, $A_{LL}$, for neutral pions produced at forward directions in
polarized proton-proton collisions, at a center-of-mass energy of $510$ GeV.
Results are given for transverse momenta in the range $2<p_{T}<10$ GeV/$c$
within two regions of pseudorapidity that span $2.65<\eta<3.9$. These results
are sensitive to the polarized gluon parton distribution function, $\Delta
g(x)$, down to the region of Bjorken $x \sim 10^{-3}$. The asymmetries observed
are less than $\pm 5 \cdot 10^{-3}$ in magnitude, and will help constrain the
contribution to the spin of the proton from polarized gluons at low $x$, when
combined with other measurements as part of a global analysis.
