Square-free values of decomposable forms

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 $\mathrm{deg}f\le 2n+2$ for all irreducible factors $f$ of $F$. This work generalizes a theorem of Greaves.

Final author's draft; accepted

Cited by in corpus (1)

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