Counting square-free values of random polynomials

TL;DR

This paper establishes that, on average, the error in counting square-free values of random polynomials grows at a rate proportional to the quartic root of the main term, providing a precise asymptotic estimate.

Contribution

It introduces a new average error bound for counting square-free polynomial values, advancing understanding of their distribution.

Findings

Error term is the quartic root of the main term on average

Provides asymptotic estimates for square-free values of polynomials

Enhances probabilistic understanding of polynomial value distributions

Abstract

We prove that the average error term when counting square-free values of polynomials is the quartic root of the main term.