论文标题
Bateman-horn，多项式chowla和Hasse原理具有概率1
Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
论文作者
论文摘要
使用概率1，我们评估了按高度订购的多项式f值的各种算术函数的平均行为。这使我们能够建立Bateman-Horn猜想的平均版本，多项式Chowla猜想，并解决有关规范形式方程的积分原理的基本问题。此外，我们能够在渐近学和特殊集合的大小中量化错误项，均以任意的对数功率节省。
With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree d polynomials f that are ordered by height. This allows us to establish averaged versions of the Bateman-Horn conjecture, the polynomial Chowla conjecture and to address a basic question about the integral Hasse principle for norm form equations. Moreover, we are able to quantify the error term in the asymptotics and the size of the exceptional set of f, both with arbitrary logarithmic power savings.
