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

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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.date.issued2013
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.en_AU
dc.description.sponsorshipThe second author was supported in part by ARC Grant DE120100173.en_AU
dc.format14 pagesen_AU
dc.identifier.issn0025-5718
dc.identifier.urihttp://hdl.handle.net/1885/11566
dc.publisherAmerican Mathematical Societyen_AU
dc.relationhttp://purl.org/au-research/grants/arc/de120100173en_AU
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/PDFen_AU
dc.sourceMathematics of Computationen_AU
dc.subjectSkewes' numberen_AU
dc.subjectprime counting functionen_AU
dc.titleA still sharper region where π(x) - li(x) is positiveen_AU
dc.typeJournal articleen_AU
local.contributor.affiliationTrudgian, Tim, Mathematical Sciences Institute, The Australian National University
local.contributor.authoruidu3958358en_AU
local.description.notesFirst published in Mathematics of Computation in [2014], published by the American Mathematical Societyen_AU
local.publisher.urlhttp://www.ams.org/journals/en_AU
local.type.statusSubmitted Versionen_AU

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