  Using molecular dynamics simulation of a standard coarse-grained polymer
glass model we investigate by means of the stress-fluctuation formalism the
shear modulus $\mu$ as a function of temperature $T$ and sampling time $\Delta
t$. While the ensemble-averaged modulus $\mu(T)$ is found to decrease
continuously for all $\Delta t$ sampled, its standard deviation $\delta \mu(T)$
is non-monotonous with a striking peak at the glass transition. Confirming the
effective time-translational invariance of our systems, $\mu(\Delta t)$ can be
understood using a weighted integral over the shear-stress relaxation modulus
$G(t)$. While the crossover of $\mu(T)$ gets sharper with increasing $\Delta
t$, the peak of $\delta \mu(T)$ becomes more singular. % It is thus elusive to
predict the modulus of a single configuration at the glass transition.
