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arXiv · 1801.04481

Density of power-free values of polynomials

Kostadinka Lapkova·Stanley Yao Xiao
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Abstract

We establish asymptotic formulae for the number of $k$-free values of polynmilas $F(x_1,\cdots,x_n)\in\mathbb{Z}[x_1,\cdots,x_n]$ of degree $d\geq 2$ for any $n\geq 1$, including when the variables are prime, as long as $k\geq (3d+1)/4$. Thus we generalize a work of Browning, while we use a different sieveing technique for the middle range of primes.

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Kostadinka Lapkova, Stanley Yao Xiao. 2018-01-13. Density of power-free values of polynomials. https://doi.org/10.1112/s0025579319000275

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