The distribution of integers with at least two divisors in a short interval

Kevin Ford; Gérald Tenenbaum

doi:10.1093/qmath/ham001

The distribution of integers with at least two divisors in a short interval

Kevin Ford, Gérald Tenenbaum

Mathematics

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

Abstract

We estimate the density of integers which have more than one divisor in an interval (y, z] with z ≈ y + y/(log y)^log4-1. As a consequence, we determine the precise range of z such that most integers which have at least one divisor in (y, z] have exactly one such divisor.

Original language	English (US)
Pages (from-to)	187-201
Number of pages	15
Journal	Quarterly Journal of Mathematics
Volume	58
Issue number	2
DOIs	https://doi.org/10.1093/qmath/ham001
State	Published - Jun 2007

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Mathematics(all)

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10.1093/qmath/ham001

Cite this

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title = "The distribution of integers with at least two divisors in a short interval",

abstract = "We estimate the density of integers which have more than one divisor in an interval (y, z] with z ≈ y + y/(log y)log4-1. As a consequence, we determine the precise range of z such that most integers which have at least one divisor in (y, z] have exactly one such divisor.",

author = "Kevin Ford and G{\'e}rald Tenenbaum",

note = "Funding Information: The first author was supported by National Science Foundation grant DMS-0301083.",

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The distribution of integers with at least two divisors in a short interval

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