Another note on smooth numbers in short intervals

: Matomaki K

Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

: 2016

: International Journal of Number Theory

: INTERNATIONAL JOURNAL OF NUMBER THEORY

: INT J NUMBER THEORY

: 12

: 2

: 323

: 340

: 18

: 1793-0421

: 1793-7310

DOI: https://doi.org/10.1142/S1793042116500196

In this paper, we prove that, for any positive constants d and e and every large enough x, the interval [x, x + root x(log x)(7/3+delta)] contains numbers whose all prime factors are smaller than x(epsilon).

Smoothshorts2.pdf