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arXiv · 1307.2481

The density of twins of $k$-free numbers

Rainer Dietmann·Oscar Marmon
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Abstract

For $k \geq 2$, we consider the number $A_k(Z)$ of positive integers $n \leq Z$ such that both $n$ and $n+1$ are $k$-free. We prove an asymptotic formula $A_k(Z) = c_k Z + O(Z^{14/(9k)+ε})$, where the error term improves upon previously known estimates. The main tool used is the approximative determinant method of Heath-Brown.

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Rainer Dietmann, Oscar Marmon. 2014-02-24. The density of twins of $k$-free numbers. https://doi.org/10.1112/blms%2Fbdu038

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