  Keating and Rudnick studied the variance of the polynomial von Mangoldt
function $\Lambda \colon \mathbb{F}_q[t] \rightarrow \mathbb{C}$ in arithmetic
progressions and short intervals using two equidistribution results by Katz.
Hall, Keating and Roditty-Gershon then generalised the result for arithmetic
progressions for a von Mangoldt function $\Lambda_\rho$ attached to a Galois
representation $\rho \colon \mathrm{Gal} (
\overline{\mathbb{F}_q(t)}/\mathbb{F}_q(t) ) \rightarrow
\mathrm{GL}_m(\overline{\mathbb{Q}}_\ell)$. We employ a recent equidistribution
result by Sawin in order to generalise the corresponding result for short
intervals for $\Lambda_\rho$.
