il The autocorrelation of the Möbius function and Chowla ’ s conjecture for the rational function field in characteristic

Let Fq be a finite field of q elements, and let Fq[x] be the polynomial ring over Fq. The Möbius function of a nonzero polynomial F ∈ Fq[x] is defined to be μ(F) = (−1)r if F = cP1 · · ·Pr with 0 = c ∈ Fq and P1, . . . , Pr are distinct monic irreducible polynomials, and μ(F) = 0 otherwise. Let Mn ⊂ Fq[x] be the set of monic polynomials of degree n over Fq, which is of size #Mn = qn. For r > 0, distinct polynomials α1, . . . ,αr ∈ Fq[x] with degαj < n, and i ∈ {1, 2}, not all even, set