# Primes in tuples IV: Density of small gaps between consecutive primes

Daniel Alan Goldston; János Pintz; Cem Yalçın Yıldırım

Acta Arithmetica (2013)

- Volume: 160, Issue: 1, page 37-53
- ISSN: 0065-1036

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topDaniel Alan Goldston, János Pintz, and Cem Yalçın Yıldırım. "Primes in tuples IV: Density of small gaps between consecutive primes." Acta Arithmetica 160.1 (2013): 37-53. <http://eudml.org/doc/279830>.

@article{DanielAlanGoldston2013,

abstract = {We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η 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.},

author = {Daniel Alan Goldston, János Pintz, Cem Yalçın Yıldırım},

journal = {Acta Arithmetica},

keywords = {consecutive primes; gaps; density},

language = {eng},

number = {1},

pages = {37-53},

title = {Primes in tuples IV: Density of small gaps between consecutive primes},

url = {http://eudml.org/doc/279830},

volume = {160},

year = {2013},

}

TY - JOUR

AU - Daniel Alan Goldston

AU - János Pintz

AU - Cem Yalçın Yıldırım

TI - Primes in tuples IV: Density of small gaps between consecutive primes

JO - Acta Arithmetica

PY - 2013

VL - 160

IS - 1

SP - 37

EP - 53

AB - We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η 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.

LA - eng

KW - consecutive primes; gaps; density

UR - http://eudml.org/doc/279830

ER -

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