  There is extensive current interest about electronic topology in correlated
settings. In strongly correlated systems, contours of Green's function zeros
may develop in frequency-momentum space, and their role in correlated topology
has increasingly been recognized. However, whether and how the zeros contribute
to electronic properties is a matter of uncertainty. Here we address the issue
in an exactly solvable model for Mott insulator. We show that the Green's
function zeros contribute to several physically measurable correlation
functions, in a way that does not run into inconsistencies. In particular, the
physical properties remain robust to chemical potential variations up to the
Mott gap as it should be based on general considerations. Our work sets the
stage for further understandings on the rich interplay among topology, symmetry
and strong correlations.
