REAL

On the ratio of consecutive gaps between primes

Pintz, János (2015) On the ratio of consecutive gaps between primes. In: Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday. Springer International Publishing, Cham (Németország), pp. 285-304. ISBN 978-331922240-0

[img]
Preview
Text
1406.2658v2.pdf

Download (243kB) | Preview

Abstract

In the present work we prove a common generalization of Maynard- Tao’s recent result about consecutive bounded gaps between primes and of the Erdős-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60-year-old problem of Erdős, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively. This is proved in the paper in a stronger form that not only dn = pn+1 - pn can be arbitrarily large compared to dn+1 but this remains true if dnC1 is replaced by the maximum of the k differences dn+1,…, dn+k for arbitrary fix k. The ratio can reach c(k) times the size of the classical Erdős-Rankin function with a constant c(k) depending only on k. © Springer International Publishing Switzerland 2015.

Item Type: Book Section
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 05 Sep 2017 13:52
Last Modified: 05 Sep 2017 13:52
URI: http://real.mtak.hu/id/eprint/61601

Actions (login required)

Edit Item Edit Item