Density of power-free values of polynomials II

Kostadinka Lapkova; Stanley Yao Xiao

Density of power-free values of polynomials II

Number Theory 2020-06-01 v1

Authors: Kostadinka Lapkova , Stanley Yao Xiao

Abstract

In this paper we prove that polynomials $F(x_1, \cdots, x_n) \in \mathbb{Z}[x_1, \cdots, x_n]$ of degree $d \geq 3$ , satisfying certain hypotheses, take on the expected density of $(d-1)$ -free values. This extends the authors' earlier result where a different method implied the similar statement for polynomials of degree $d\geq 5$ .

Keywords

power-free values polynomials number theory density Diophantine equations

Cite

@article{arxiv.2005.14655,
  title  = {Density of power-free values of polynomials II},
  author = {Kostadinka Lapkova and Stanley Yao Xiao},
  journal= {arXiv preprint arXiv:2005.14655},
  year   = {2020}
}

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