Journal article
Small gaps between primes
- Abstract:
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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
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- Files:
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(Author's original, pdf, 252.4KB)
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- Publisher copy:
- 10.4007/annals.2015.181.1.7
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Authors
Bibliographic Details
- 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:
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0003-486X
Item Description
- Keywords:
- Pubs id:
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pubs:518918
- UUID:
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uuid:cb2fe59b-360d-4c22-9ec9-755af56398d4
- Local pid:
- pubs:518918
- Deposit date:
- 2016-10-17
Terms of use
- Copyright holder:
- Department of Mathematics, Princeton University
- Copyright date:
- 2015
- Notes:
-
This is a
pre-print version of a journal article published by The Department of Mathematics, Princeton University in Annals of Mathematics on 2015-01-01, available online: http://dx.doi.org/10.4007/annals.2015.181.1.7
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