- Abstract:
- We prove a generalization of the author's work to show that any subset of the primes which is 'well distributed' in arithmetic progressions contains many primes which are close together. Moreover, our bounds hold with some uniformity in the parameters. As applications, we show there are infinitely many intervals of length containing primes, and show lower bounds of the correct order of magnitude for the number of strings of congruent primes with.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted manuscript
- Files:
-
-
(pdf, 362.6kb)
-
- Publisher copy:
- 10.1112/S0010437X16007296
-
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- Publisher:
- Cambridge University Press Publisher's website
- Journal:
- Compositio Mathematica Journal website
- Volume:
- 152
- Issue:
- 7
- Pages:
- 1517-1554
- Publication date:
- 2016-04-01
- Acceptance date:
- 2015-10-15
- DOI:
- ISSN:
-
0010-437X and 1570-5846
- Pubs id:
-
pubs:618344
- URN:
-
uri:a08a24aa-e17c-4323-8aea-a1782d68c694
- UUID:
-
uuid:a08a24aa-e17c-4323-8aea-a1782d68c694
- Local pid:
- pubs:618344
- Paper number:
- 7
- Keywords:
- Copyright holder:
- James Maynard
- Copyright date:
- 2016
- Notes:
-
This is an
accepted manuscript of a journal article published by Cambridge University Press in Compositio Mathematica on 2016-04-01, available online: http://dx.doi.org/10.1112/S0010437X16007296
Journal article
Dense clusters of primes in subsets
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