A note on exponential-Möbius sums over Fq[t]

In 1991, Baker and Harman proved, under the assumption of the generalized Riemann hypothesis, thatmaxθ∈[0,1)⁡|∑n⩽xμ(n)e(nθ)|≪ϵx3/4+ϵ. The purpose of this note is to deduce an analogous bound in the context of polynomials over a finite field using Weil's Riemann Hypothesis for curves over a finite field. Our approach is based on the work of Hayes who studied exponential sums over irreducible polynomials.