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DENSITY OF POWER-FREE VALUES OF POLYNOMIALS

  • Kostadinka Lapkova (a1) and Stanley Yao Xiao (a2)

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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DENSITY OF POWER-FREE VALUES OF POLYNOMIALS

  • Kostadinka Lapkova (a1) and Stanley Yao Xiao (a2)

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