LINEAR AND QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION OVER Fq[t]

We examine correlations of the Möbius function over Fq[t] with linear or quadratic phases, that is, averages of the form 11qn∑deg f0 if Q is quadratic. The latter bound may be reduced to O(q−c'n) for some c'>0 when Q(f) is a linear form in the coefficients of f2, that is, a Hankel quadratic form, whereas, for general quadratic forms, it relies on a bilinear version of the additive‐combinatorial Bogolyubov theorem.