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Dense clusters of primes in subsets

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

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Publisher copy:
10.1112/S0010437X16007296

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Department:
Oxford, MPLS, Mathematical Institute
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

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