A lower bound on the mean value of the Erdős–Hooley Delta function

Kevin Ford; Dimitris Koukoulopoulos; Terence Tao

doi:10.1112/plms.12618

A lower bound on the mean value of the Erdős–Hooley Delta function

Kevin Ford, Dimitris Koukoulopoulos, Terence Tao

Research output: Contribution to journal › Article › peer-review

Abstract

We give an improved lower bound for the average of the Erdős–Hooley function (Formula presented.), namely (Formula presented.) for all (Formula presented.) and any fixed (Formula presented.), where (Formula presented.) is an exponent previously appearing in work of Green and the first two authors. This improves on a previous lower bound of (Formula presented.) of Hall and Tenenbaum, and can be compared to the recent upper bound of (Formula presented.) of the second and third authors.

Original language	English (US)
Article number	e12618
Journal	Proceedings of the London Mathematical Society
Volume	129
Issue number	1
Early online date	Jun 30 2024
DOIs	https://doi.org/10.1112/plms.12618
State	Published - Jul 2024
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1112/plms.12618License: CC BY

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abstract = "We give an improved lower bound for the average of the Erd{\H o}s–Hooley function (Formula presented.), namely (Formula presented.) for all (Formula presented.) and any fixed (Formula presented.), where (Formula presented.) is an exponent previously appearing in work of Green and the first two authors. This improves on a previous lower bound of (Formula presented.) of Hall and Tenenbaum, and can be compared to the recent upper bound of (Formula presented.) of the second and third authors.",

author = "Kevin Ford and Dimitris Koukoulopoulos and Terence Tao",

note = "K. Ford was supported by National Science Foundation Grants DMS\u20101802139 and DMS\u20102301264. D. Koukoulopoulos was supported by the Courtois Chair II in fundamental research, the Natural Sciences and Engineering Research Council of Canada (RGPIN\u20102018\u201005699) and the Fonds de recherche du Qu\u00E9bec \u2013 Nature et technologies (2022\u2010PR\u2010300951). T. Tao was supported by NSF grant DMS\u20101764034.",

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A lower bound on the mean value of the Erdős–Hooley Delta function

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