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

• Autorzy: Daniel Alan Goldston , János Pintz , Cem Yalçın Yıldırım
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11N05: Distribution of primes
• 11N36: Applications of sieve methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 160
• Numer: 1
• Strony: 37-53

Daty

wydano

2013

Twórcy

autor

Daniel Alan Goldston

• Department of Mathematics, San Jose State University, San Jose, CA 95192, U.S.A.

autor

János Pintz

• Rényi Mathematical Institute, of the Hungarian Academy of Sciences, H-1364 Budapest, Pf 127, Hungary

autor

Cem Yalçın Yıldırım

• Department of Mathematics, Boğaziçi University, Bebek, İstanbul 34342, Turkey

Identyfikatory

DOI

10.4064/aa160-1-3