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

Daniel 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 -