INTEGERS, WITHOUT LARGE PRIME FACTORS, IN ARITHMETIC PROGRESSIONS .2.

Authors
GRANVILLE A
Citation
A. Granville, INTEGERS, WITHOUT LARGE PRIME FACTORS, IN ARITHMETIC PROGRESSIONS .2., Philosophical transactions-Royal Society of London. Physical sciences and engineering, 345(1676), 1993, pp. 349-362
Citations number
9
Categorie Soggetti
Multidisciplinary Sciences
Journal title
Philosophical transactions-Royal Society of London. Physical sciences and engineering → ACNP
ISSN journal
09628428
Volume
345
Issue
1676
Year of publication
1993
Pages
349 - 362
Database
ISI
SICI code
0962-8428(1993)345:1676<349:IWLPFI>2.0.ZU;2-D
Abstract
We show that, for any fixed epsilon > 0, there are asymptotically the same number of integers up to x, that are composed only of primes less -than-or-equal-to y, in each arithmetic progression (mod q), provided that y greater-than-or-equal-to q1+epsilon and log x/log q --> infinit y as y --> infinity : this improves on previous estimates.