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arXiv · 1103.2028

Powerfree Values of Polynomials

D. R. Heath-Brown
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Abstract

For irreducible integer polynomials $f(n)=n^d+c$ we prove an asymptotic formula for the number of $k$-th power free values taken by $f(n)$, for $n$ running up to $x$, subject to the condition $k\ge (5d+3)/9$. This improves earlier results in which the condition was $k\ge (3d+1)/4$. We also show that one can handle $f(p)$ for prime arguments $p$, for the same range of $k$.

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D. R. Heath-Brown. 2011-03-10. Powerfree Values of Polynomials. https://arxiv.org/abs/1103.2028

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