T. D. Browning

Bateman–Horn, polynomial Chowla and the Hasse principle with probability 1

Abstract With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree 𝑑 polynomials f ∈ Z ⁢ [ t ] f\in\mathbb{Z}[t] that are ordered by height. This allows us to establish averaged versions of the Bateman–Horn conjecture, the polynom...