Journal article

### Small gaps between primes

Abstract:

We introduce a refinement of the GPY sieve method for studying prime kk-tuples and small gaps between primes. This refinement avoids previous limitations of the method and allows us to show that for each kk, the prime kk-tuples conjecture holds for a positive proportion of admissible kk-tuples. In particular, lim infn(pn+m−pn)<∞lim infn(pn+m−pn)<∞ for every integer mm. We also show that lim inf(pn+1−pn)≤600lim inf(pn+1−pn)≤600 and, if we assume the Elliott-Halberstam conjecture, that li...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Author's original, pdf, 252.4KB)
Publisher copy:
10.4007/annals.2015.181.1.7

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Princeton University, Department of Mathematics Publisher's website
Journal:
Annals of Mathematics Journal website
Volume:
181
Issue:
1
Pages:
383-413
Publication date:
2015-01-01
Acceptance date:
2014-03-25
DOI:
ISSN:
0003-486X
Keywords:
Pubs id:
pubs:518918
UUID:
uuid:cb2fe59b-360d-4c22-9ec9-755af56398d4
Local pid:
pubs:518918
Deposit date:
2016-10-17