Square-root cancellation for sums of factorization functions over squarefree progressions in F_q [t]

We prove estimates for the level of distribution of the Möbius function, von Mangoldt function, and divisor functions in squarefree progressions in the ring of polynomials over a finite field. Each level of distribution converges to 1 as q goes to c∞, and the power savings converges to square- root cancellation as q goes to co. These results in fact apply to a more general class of functions, the factorization functions, that includes these three. The divisor estimates have applications to the moments of L-functions, and the von Mangoldt estimate to 1 -level densities.