Square-free Values of Decomposable Forms

Stanley Yao Xiao
2018 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
In this paper we prove that decomposable forms, or homogeneous polynomials $F(x_1, \cdots, x_n)$ with integer coefficients which split completely into linear factors over $\mathbb{C}$, take on infinitely many square-free values subject to simple necessary conditions and $\operatorname{deg} f \leq 2n + 2$ for all irreducible factors $f$ of $F$. This work generalizes a theorem of Greaves.
doi:10.4153/cjm-2017-060-4 fatcat:mh2osrgt7fbcvhyfupppfvdthm