Green–Tao theorem in function fields
Thái Hoàng Lê · Acta Arithmetica · 2011
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\mathbf{F}_q[t]$ contain configurations of the form $\{f+ Pg : \d(P)<k \}, g eq 0$.