Hardy-littlewood tuple conjecture over large finite fields

We prove the following function field analog of the Hardy-Littlewood conjecture (which generalizes the twin prime conjecture) over large finite fields. Let n and r be positive integers and q an odd prime power. For a tuple of distinct polynomials of degree <n let π(q,n;a) be the number of monic polynomials of degree n such that f+a₁,f+a_r are simultaneously irreducible. We prove that as and n,r fixed.