MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Bounded gaps between primes in short intervals

Author(s)
Alweiss, Ryan; Luo, Sammy
Thumbnail
Download40993_2018_109_ReferencePDF.pdf (373.4Kb)
Publisher Policy

Publisher Policy

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.

Terms of use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Metadata
Show full item record
Abstract
Abstract Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $$[x-x^{0.525},x]$$ [ x - x 0.525 , x ] for large x. In this paper, we extend a result of Maynard and Tao concerning small gaps between primes to intervals of this length. More precisely, we prove that for any $$\delta \in [0.525,1]$$ δ ∈ [ 0.525 , 1 ] there exist positive integers k, d such that for sufficiently large x, the interval $$[x-x^\delta ,x]$$ [ x - x δ , x ] contains $$\gg _{k} \frac{x^\delta }{(\log x)^k}$$ ≫ k x δ ( log x ) k pairs of consecutive primes differing by at most d. This confirms a speculation of Maynard that results on small gaps between primes can be refined to the setting of short intervals of this length.
Date issued
2018-03-19
URI
https://hdl.handle.net/1721.1/131478
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Springer International Publishing
Citation
Research in Number Theory. 2018 Mar 19;4(2):15
Version: Author's final manuscript

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.