  We investigate a function field analogue of a recent conjecture on
autocorrelations of sums of two squares by Freiberg, Kurlberg and Rosenzweig,
which generalizes an older conjecture by Connors and Keating. In particular, we
provide extensive numerical evidence and prove it in the large finite field
limit. Our method can also handle correlations of other arithmetic functions
and we give applications to (function field analogues of) the average of sums
of two squares on shifted primes, and to autocorrelations of higher divisor
functions twisted by a quadratic character.
