English

Consecutive square-free values for some polynomials

Number Theory 2023-05-09 v1

Abstract

In this paper we study the distribution of consecutive square-free numbers of the forms x2+y2+z+1x^2+y^2+z+1, x2+y2+z+2x^2+y^2+z+2 and x2+y2+z2+z+1x^2+y^2+z^2+z+1, x2+y2+z2+z+2x^2+y^2+z^2+z+2, respectively. We establish asymptotic formulas for each of these two cases.

Cite

@article{arxiv.2305.04020,
  title  = {Consecutive square-free values for some polynomials},
  author = {S. I. Dimitrov},
  journal= {arXiv preprint arXiv:2305.04020},
  year   = {2023}
}
R2 v1 2026-06-28T10:27:38.941Z