On moments of the Erdős--Hooley Delta-function
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912751485452288 |
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| author | de la Bretèche, R. Tenenbaum, G. |
| author_facet | de la Bretèche, R. Tenenbaum, G. |
| contents | For integer $n\geqslant 1$ and real $u$, let $Δ(n,u):=|\{d:d\mid n,\,{\rm e}^u<d\leqslant {\rm e}^{u+1}\}|$. The Erdős--Hooley Delta-function is then defined by $Δ(n):=\max_{u\in{\mathbb R}}Δ(n,u).$ We provide new upper bounds for weighted real moments of this function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On moments of the Erdős--Hooley Delta-function de la Bretèche, R. Tenenbaum, G. Number Theory primary 11N37, secondary 11K65 For integer $n\geqslant 1$ and real $u$, let $Δ(n,u):=|\{d:d\mid n,\,{\rm e}^u<d\leqslant {\rm e}^{u+1}\}|$. The Erdős--Hooley Delta-function is then defined by $Δ(n):=\max_{u\in{\mathbb R}}Δ(n,u).$ We provide new upper bounds for weighted real moments of this function. |
| title | On moments of the Erdős--Hooley Delta-function |
| topic | Number Theory primary 11N37, secondary 11K65 |
| url | https://arxiv.org/abs/2512.05652 |