On the friable mean-value of the Erdős-Hooley Delta function
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916180986429440 |
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| author | Martin, Bruno Tenenbaum, Gérald Wetzer, Julie |
| author_facet | Martin, Bruno Tenenbaum, Gérald Wetzer, Julie |
| contents | For integer $n$ and real $u$, define $Δ(n,u):= |\{d : d \mid n,\,{\rm e}^u <d\leqslant {\rm e}^{u+1} \}|$. Then, put $ Δ(n):=\max_{u\in{\mathbb R}} Δ(n,u).$ We provide uniform upper and lower bounds for the mean-value of $Δ(n)$ over friable integers, i.e. integers free of large prime factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05530 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the friable mean-value of the Erdős-Hooley Delta function Martin, Bruno Tenenbaum, Gérald Wetzer, Julie Number Theory 11N25, 11N37 For integer $n$ and real $u$, define $Δ(n,u):= |\{d : d \mid n,\,{\rm e}^u <d\leqslant {\rm e}^{u+1} \}|$. Then, put $ Δ(n):=\max_{u\in{\mathbb R}} Δ(n,u).$ We provide uniform upper and lower bounds for the mean-value of $Δ(n)$ over friable integers, i.e. integers free of large prime factors. |
| title | On the friable mean-value of the Erdős-Hooley Delta function |
| topic | Number Theory 11N25, 11N37 |
| url | https://arxiv.org/abs/2307.05530 |