On the Chowla and twin primes conjectures over F_q[T]

Using geometric methods, we improve on the function field version of the Burgess bound and show that, when restricted to certain special subspaces, the Möbius function over F_q[T] can be mimicked by Dirichlet characters. Combining these, we obtain a level of distribution close to 1 for the Möbius function in arithmetic progressions and resolve Chowla's k-point correlation conjecture with large uniformity in the shifts. Using a function field variant of a result by Fouvry-Michel on exponential sums involving the Möbius function, we obtain a level of distribution beyond 1=2 for irreducible polynomials, and establish the twin prime conjecture in a quantitative form.