A1 Refereed original research article in a scientific journal
A NOTE ON SMOOTH NUMBERS IN SHORT INTERVALS
Authors: Matomäki Kaisa
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
Publication year: 2010
Journal:International Journal of Number Theory
Journal name in sourceINTERNATIONAL JOURNAL OF NUMBER THEORY
Journal acronym: INT J NUMBER THEORY
Number in series: 5
Volume: 6
Issue: 5
First page : 1113
Last page: 1116
Number of pages: 4
ISSN: 1793-0421
DOI: https://doi.org/10.1142/S1793042110003381
Abstract
We prove that, for any epsilon > 0, there exists a constant C > 0 such that the interval [x, x + C root x] contains numbers whose all prime factors are smaller than x(1/(5 root e)+epsilon).
We prove that, for any epsilon > 0, there exists a constant C > 0 such that the interval [x, x + C root x] contains numbers whose all prime factors are smaller than x(1/(5 root e)+epsilon).
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