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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...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Author's Original

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Publisher copy:
10.4007/annals.2015.181.1.7

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Department:
Oxford, MPLS, Mathematical Institute
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
Acceptance date:
2014-03-25
DOI:
ISSN:
0003-486X
Pubs id:
pubs:518918
URN:
uri:cb2fe59b-360d-4c22-9ec9-755af56398d4
UUID:
uuid:cb2fe59b-360d-4c22-9ec9-755af56398d4
Local pid:
pubs:518918
Keywords:

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