Granville, A;
Koukoulopoulos, D;
Matomaki, K;
(2015)
When the sieve works.
Duke Mathematical Journal
, 164
(10)
pp. 1935-1969.
10.1215/00127094-3120891.
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Abstract
We are interested in classifying those sets of primes PP such that when we sieve out the integers up to xx by the primes in PcPc we are left with roughly the expected number of unsieved integers. In particular, we obtain the first general results for sieving an interval of length xx with primes including some in (x−−√,x](x,x], using methods motivated by additive combinatorics.
| Type: | Article |
|---|---|
| Title: | When the sieve works |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1215/00127094-3120891 |
| Publisher version: | http://doi.org/10.1215/00127094-3120891 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1497586 |
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