Dense clusters of primes in subsets
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 a...
| Main Author: | |
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| Format: | Journal article |
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Cambridge University Press
2016
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| _version_ | 1797085578757406720 |
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| author | Maynard, J |
| author_facet | Maynard, J |
| author_sort | Maynard, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:10:41Z |
| format | Journal article |
| id | oxford-uuid:a08a24aa-e17c-4323-8aea-a1782d68c694 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:10:41Z |
| publishDate | 2016 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:a08a24aa-e17c-4323-8aea-a1782d68c6942022-03-27T02:06:14ZDense clusters of primes in subsetsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a08a24aa-e17c-4323-8aea-a1782d68c694Symplectic Elements at OxfordCambridge University Press2016Maynard, JWe 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. |
| spellingShingle | Maynard, J Dense clusters of primes in subsets |
| title | Dense clusters of primes in subsets |
| title_full | Dense clusters of primes in subsets |
| title_fullStr | Dense clusters of primes in subsets |
| title_full_unstemmed | Dense clusters of primes in subsets |
| title_short | Dense clusters of primes in subsets |
| title_sort | dense clusters of primes in subsets |
| work_keys_str_mv | AT maynardj denseclustersofprimesinsubsets |