Primes in tuples. IV: Density of small gaps between consecutive primes (Q2840495)

We can only quote the authors' perfect abstract: 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.''NEWLINENEWLINEIn fact, a bigger review in this small space could not adequately describe the wealth of results of this paper (and of other papers in the series).NEWLINENEWLINE NEWLINEFor Part III see [the authors, Funct. Approximatio, Comment. Math. 35, 79--89 (2006; Zbl 1196.11123)].