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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

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Publisher copy:
10.1112/S0010437X16007296

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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:
1570-5846 and 0010-437X
Keywords:
Pubs id:
pubs:618344
UUID:
uuid:a08a24aa-e17c-4323-8aea-a1782d68c694
Local pid:
pubs:618344
Deposit date:
2016-10-17

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