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Square-free values of decomposable forms

  • Stanley Yao Xiao,
    Mathematical Institute, University of Oxford, Oxford, UK
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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 $\deg f \leq 2n + 2$ for all irreducible factors $f$ of $F$. This work generalizes a theorem of Greaves.
Keywords: square-free value, decomposable form, Selberg sieve square-free value, decomposable form, Selberg sieve
MSC Classifications: 11B05 show english descriptions Density, gaps, topology 11B05 - Density, gaps, topology
 

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