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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Podrobná bibliografie
Vydáno v:Proceedings of the London Mathematical Society Ročník 95; číslo 3; s. 653 - 686
Hlavní autoři: Goldston, D. A., Y ld r m, C. Y.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford University Press 01.11.2007
ISSN:0024-6115, 1460-244X
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Popis
Shrnutí: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.
Bibliografie: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