Geodesic
Primes in tuples IV: Density of small gaps between consecutive primes
Daniel Alan Goldston1 ; János Pintz2 ; Cem Yalçın Yıldırım3
1 Department of Mathematics San Jose State University San Jose, CA 95192, U.S.A.
2 Rényi Mathematical Institute of the Hungarian Academy of Sciences H-1364 Budapest, Pf 127, Hungary
3 Department of Mathematics Boğaziçi University Bebek, İstanbul 34342, Turkey
Acta Arithmetica, Tome 160 (2013) no. 1, pp. 37-53 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove that given any small but fixed $\eta > 0$, a positive proportion of all gaps between consecutive primes are smaller than $\eta $ times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on $\eta $ is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.
DOI : 10.4064/aa160-1-3
Keywords: prove given small fixed eta positive proportion gaps between consecutive primes smaller eta times average gap unconditional conditional quantitative results vein results dependence eta given explicitly providing quantitative addition first paper series measuring effect knowledge level distribution primes

Daniel Alan Goldston 1 ; János Pintz 2 ; Cem Yalçın Yıldırım 3

1 Department of Mathematics San Jose State University San Jose, CA 95192, U.S.A.
2 Rényi Mathematical Institute of the Hungarian Academy of Sciences H-1364 Budapest, Pf 127, Hungary
3 Department of Mathematics Boğaziçi University Bebek, İstanbul 34342, Turkey 
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     title = {Primes in tuples {IV:} {Density} of small gaps
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     journal = {Acta Arithmetica},
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 between consecutive primes
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Daniel Alan Goldston; János Pintz; Cem Yalçın Yıldırım. Primes in tuples IV: Density of small gaps
 between consecutive primes. Acta Arithmetica, Tome 160 (2013) no. 1, pp. 37-53. doi: 10.4064/aa160-1-3

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