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Comment on "On the squarefree density of polynomials"

Yuri G. Zarhin

Abstract

This is an exposition of results of R.C. Vaughan and the author (Mathematika 70 (2024), no. 4). We discuss how often the squarefree values of an integral polynomial do occur. We discuss interrelations between our results and results of B. Poonen (arXiv:math/0203292 [math.NT]).

Comment on "On the squarefree density of polynomials"

Abstract

This is an exposition of results of R.C. Vaughan and the author (Mathematika 70 (2024), no. 4). We discuss how often the squarefree values of an integral polynomial do occur. We discuss interrelations between our results and results of B. Poonen (arXiv:math/0203292 [math.NT]).

Paper Structure

This paper contains 1 section, 3 theorems, 10 equations.

Table of Contents

  1. Main results

Key Result

Theorem 1.1

If $\mathcal{P}$ does not satisfy property (a) then the Euler product $\mathfrak{S}_{\mathcal{P}} \ne 0$if and only if$\mathcal{P}$ is squarefree.

Theorems & Definitions (4)

  • Remark 1
  • Theorem 1.1
  • Corollary 1.2
  • Corollary 1.3