English

Power-free values of binary forms and the global determinant method

Number Theory 2017-12-25 v2

Abstract

We give an improved estimate for the density of kk-free values of integral binary forms with no fixed kk-th power divisor. Further, we give the corresponding improvement to a theorem of Stewart and Top on the number of power-free values in an interval that may be assumed by a binary form. The approach we use involves a generalization of the global determinant method of Salberger.

Keywords

Cite

@article{arxiv.1505.05587,
  title  = {Power-free values of binary forms and the global determinant method},
  author = {Stanley Yao Xiao},
  journal= {arXiv preprint arXiv:1505.05587},
  year   = {2017}
}

Comments

45 pages; final accepted version

R2 v1 2026-06-22T09:38:27.865Z