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Sieving the positive integers by large primes (1988)
by
D. A. Goldston
,
Kevin S. McCurley
| Citations: | 4 - 0 self |
BibTeX
@MISC{Goldston88sievingthe,
author = {D. A. Goldston and Kevin S. McCurley},
title = {Sieving the positive integers by large primes},
year = {1988}
}
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Abstract
Let Q be a set of primes having relative density 6 among the primes, with 0~6 < 1, and let $(x. y. Q) be the number of positive integers <x that have no prime factors from Q exceeding y. We prove that if y-t cc, then r&x, y, Q) w xp6(u), where u = (log x)/(log y), and ps is the continuous solution of the differential delay equation up&(u) =-6p,(u- 1), p&(u) = 1, 0 < I ( < 1. This generalizes work by Dickman, de Bruijn, and Hildebrand, who considered the case where Q consists of all primes (and 6 = 1).
