Skip navigation
Skip navigation

A still sharper region where π(x) - li(x) is positive

Download (240.75 kB)

Saouter, Yannick; Trudgian, Tim; Demichel, Patrick

Description

We consider the least number x for which a change of sign of π(x) - li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new lower bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.

dc.contributor.authorSaouter, Yannick
dc.contributor.authorTrudgian, Tim
dc.contributor.authorDemichel, Patrick
dc.date.accessioned2014-04-11T05:14:10Z
dc.date.available2014-04-11T05:14:10Z
dc.identifier.issn0025-5718
dc.identifier.urihttp://hdl.handle.net/1885/11566
dc.description.abstractWe consider the least number x for which a change of sign of π(x) - li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new lower bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.
dc.description.sponsorshipThe second author was supported in part by ARC Grant DE120100173.
dc.format14 pages
dc.publisherAmerican Mathematical Society
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/0025-5718/author can archive pre-print (ie pre-refereeing); author can archive post-print (ie final draft post-refereeing); author can archive publisher's version/PDF
dc.sourceMathematics of Computation
dc.subjectSkewes' number
dc.subjectprime counting function
dc.titleA still sharper region where π(x) - li(x) is positive
dc.typeJournal article
local.description.notesFirst published in Mathematics of Computation in [2014], published by the American Mathematical Society
dc.date.issued2013
local.publisher.urlhttp://www.ams.org/journals/
local.type.statusSubmitted Version
local.contributor.affiliationTrudgian, Tim, Mathematical Sciences Institute, The Australian National University
dc.relationhttp://purl.org/au-research/grants/arc/de120100173
CollectionsANU Research Publications

Download

File Description SizeFormat Image
Saouter et al A still sharper region 2014.pdf240.75 kBAdobe PDFThumbnail
Show simple item record


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  17 November 2022/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator