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arXiv · 2307.05530

On the friable mean-value of the Erd\H{o}s-Hooley Delta function

Bruno Martin·Gérald Tenenbaum·Julie Wetzer
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Abstract

For integer $n$ and real $u$, define $\Delta(n,u):= |\{d : d \mid n,\,{\rm e}^u <d\leqslant {\rm e}^{u+1} \}|$. Then, put $ \Delta(n):=\max_{u\in{\mathbb R}} \Delta(n,u).$ We provide uniform upper and lower bounds for the mean-value of $\Delta(n)$ over friable integers, i.e. integers free of large prime factors.

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Bruno Martin, Gérald Tenenbaum, Julie Wetzer. 2023-07-07. On the friable mean-value of the Erd\H{o}s-Hooley Delta function. https://arxiv.org/abs/2307.05530

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