On the friable mean-value of the Erdős-Hooley Delta function

Fuente: arXiv
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Hauptverfasser: Martin, Bruno, Tenenbaum, Gérald, Wetzer, Julie
Format: Preprint
Veröffentlicht: 2023
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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