Worse than square-root cancellation in Bateman-Horn's conjecture

TL;DR

This paper establishes asymptotic results for the average error term in Bateman-Horn's conjecture specifically within the exponential range, advancing understanding of its accuracy.

Contribution

It provides the first asymptotic analysis of the average error term in Bateman-Horn's conjecture in the exponential range.

Findings

Derived asymptotics for the average error term

Identified the behavior of errors in the exponential range

Enhanced theoretical understanding of Bateman-Horn's conjecture

Abstract

We prove asymptotics for the average error term in Bateman-Horn's conjecture in the exponential range.