An upper bound on the mean value of the Erdős–Hooley Delta function

Dimitris Koukoulopoulos, Terence Tao

Type: Article

Publication Date: 2023-11-09

Citations: 3

DOI: https://doi.org/10.1112/plms.12572

Abstract

Abstract The Erdős–Hooley Delta function is defined for as . We prove that for all . This improves on earlier work of Hooley, Hall–Tenenbaum, and La Bretèche–Tenenbaum.

Locations

Proceedings of the London Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
Proceedings of the London Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
Proceedings of the London Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF

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+	On the friable mean-value of the Erdős–Hooley Delta function	2024	Bruno Martin Gérald Tenenbaum J.M. Wetzer
+ PDF	An upper bound on the mean value of the Erdős–Hooley Delta function	2023	Dimitris Koukoulopoulos Terence Tao
+ PDF	A lower bound on the mean value of the Erdős–Hooley Delta function	2024	Kevin Ford Dimitris Koukoulopoulos Terence Tao

Works Cited by This (14)

Action	Title	Year	Authors
+ PDF	On the number of restricted prime factors of an integer. I	1976	Karl K. Norton
+ PDF	Generalized Smirnov statistics and the distribution of prime factors	2007	Kevin Ford
+	On a New Technique and Its Applications to the Theory of Numbers	1979	C. Hooley
+	The average orders of Hooley's Δ <sub>r</sub> ‐functions	1984	R. R. Hall Gérald Tenenbaum
+	On the Normal Concentration of Divisors	1985	Helmut Maier Gérald Tenenbaum
+	On the Average and Normal Orders of Hooley's Δ-Function	1982	R. R. Hall Gérald Tenenbaum
+	Squares In Sumsets	2010	Hoi H. Nguyen Van H. Vu
+ PDF	Répartition des nombres superabondants	1975	P. Erdős Jean-Louis Nicolas
+ PDF	Sur le nombre des entiers représentables comme somme de trois puissances	2011	Olivier Robert
+ PDF	Equal sums in random sets and the concentration of divisors	2023	Kevin Ford Ben Green Dimitris Koukoulopoulos