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arXiv · 1612.08028

Square-free values of decomposable forms

Stanley Yao Xiao
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Abstract

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.

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Stanley Yao Xiao. 2016-12-23. Square-free values of decomposable forms. https://doi.org/10.4153/cjm-2017-060-4

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