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The differences between consecutive smooth numbers

Volume 184 / 2018

D. R. Heath-Brown Acta Arithmetica 184 (2018), 267-285 MSC: Primary 11N25; Secondary 11N36. DOI: 10.4064/aa170913-11-7 Published online: 10 August 2018


We show that large gaps between smooth numbers are infrequent. The key new tool is a novel mean value bound for a special type of Dirichlet polynomial.


  • D. R. Heath-BrownMathematical Institute
    Radcliffe Observatory Quarter
    Woodstock Road
    Oxford, OX2 6GG, UK

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