  The auto-correlations of arithmetic functions, such as the von Mangoldt
function, the M\"obius function and the divisor function, are the subject of
classical problems in analytic number theory. The function field analogues of
these problems have recently been resolved in the limit of large finite field
size $q$. However, in this limit the correlations disappear: the arithmetic
functions become uncorrelated. We compute averages of terms of lower order in
$q$ which detect correlations. Our results show that there is considerable
cancellation in the averaging and have implications for the rate at which
correlations disappear when $q \rightarrow\infty$; in particular one cannot
expect remainder terms that are of the order of the square-root of the main
term in this context.
