The Bateman-Horn conjecture predicts the fraction of integers n such that n2+1 is prime, and makes similar predictions for polynomials of higher degree. In joint work in progress with Mark Shusterman, we prove an analogue of the n2+1 case, replacing natural numbers n with polynomials in đť”˝q[u], which for instance counts the fraction of polynomials f such that f2+u is an irreducible polynomial. The proof combines geometric methods, unusual algebraic properties of polynomials, and some (very) classical number theory.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
