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DENSITY OF POWER-FREE VALUES OF POLYNOMIALS
Published online by Cambridge University Press: 14 August 2019
Abstract
We establish asymptotic formulae for the number of $k$-free values of square-free polynomials
$F(x_{1},\ldots ,x_{n})\in \mathbb{Z}[x_{1},\ldots ,x_{n}]$ of degree
$d\geqslant 2$ for any
$n\geqslant 1$, including when the variables are prime, as long as
$k\geqslant (3d+1)/4$. This generalizes a work of Browning.
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- Research Article
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- Copyright © University College London 2019
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