A NOTE ON SMOOTH NUMBERS IN SHORT INTERVALS



: Matomäki Kaisa

Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

: 2010

: International Journal of Number Theory

: INTERNATIONAL JOURNAL OF NUMBER THEORY

: INT J NUMBER THEORY

: 5

: 6

: 5

: 1113

: 1116

: 4

: 1793-0421

DOI: https://doi.org/10.1142/S1793042110003381


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).



Last updated on 2024-26-11 at 17:16