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

Kevin Ford, Gérald Tenenbaum

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)187-201
Number of pages15
JournalQuarterly Journal of Mathematics
Volume58
Issue number2
DOIs
StatePublished - Jun 2007

ASJC Scopus subject areas

  • Mathematics(all)

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