Higher correlations of divisor sums related to primes III: small gaps between primes
We use divisor sums to approximate prime tuples and moments for primes in short intervals. By connecting these results to classical moment problems we are able to prove that, for any η > 0, a positive proportion of consecutive primes are within 14+η times the average spacing between primes.
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| Published in: | Proceedings of the London Mathematical Society Vol. 95; no. 3; pp. 653 - 686 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford University Press
01.11.2007
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| ISSN: | 0024-6115, 1460-244X |
| Online Access: | Get full text |
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| Summary: | We use divisor sums to approximate prime tuples and moments for primes in short intervals. By connecting these results to classical moment problems we are able to prove that, for any η > 0, a positive proportion of consecutive primes are within 14+η times the average spacing between primes. |
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| Bibliography: | 2000 Mathematics Subject Classification 11N05 (primary), 11P32 (secondary). istex:FAE38CCC1107A2655833BFD22F20DD44694C40F2 ArticleID:pdm021 ark:/67375/HXZ-SKDSLH8J-6 2000 Mathematics Subject Classification The research of Goldston was supported by NSF; that of Yıldırım was supported by TÜBÏTAK 11N05 (primary), 11P32 (secondary). |
| ISSN: | 0024-6115 1460-244X |
| DOI: | 10.1112/plms/pdm021 |