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Article: Sign Changes of E(T), Δ(x), and P(x)

TitleSign Changes of E(T), Δ(x), and P(x)
Authors
Issue Date1994
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt
Citation
Journal Of Number Theory, 1994, v. 49 n. 1, p. 73-83 How to Cite?
AbstractLet Δ(x), P(x), and E(T) denote the usual error terms in the divisor problem, the circle problem, and the mean value theorem for |ζ( 1 2 + it)| 2. It is not hard to prove that, for a suitable constant C, each of these error terms changes sign on every interval [K, K + C √K]. We show, in contrast, that a positive proportion of intervals [K, K + C √K (log K) -5] contain no such sign change. In the case of E(T) this disproves a conjecture of A. Ivić and H. J. J. te Riele (Math. Comp.56, 1991, 303-328). © 1994 Academic Press. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156047
ISSN
2015 Impact Factor: 0.596
2015 SCImago Journal Rankings: 0.858
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHeathbrown, DRen_US
dc.contributor.authorTsang, Ken_US
dc.date.accessioned2012-08-08T08:40:11Z-
dc.date.available2012-08-08T08:40:11Z-
dc.date.issued1994en_US
dc.identifier.citationJournal Of Number Theory, 1994, v. 49 n. 1, p. 73-83en_US
dc.identifier.issn0022-314Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/156047-
dc.description.abstractLet Δ(x), P(x), and E(T) denote the usual error terms in the divisor problem, the circle problem, and the mean value theorem for |ζ( 1 2 + it)| 2. It is not hard to prove that, for a suitable constant C, each of these error terms changes sign on every interval [K, K + C √K]. We show, in contrast, that a positive proportion of intervals [K, K + C √K (log K) -5] contain no such sign change. In the case of E(T) this disproves a conjecture of A. Ivić and H. J. J. te Riele (Math. Comp.56, 1991, 303-328). © 1994 Academic Press. All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnten_US
dc.relation.ispartofJournal of Number Theoryen_US
dc.titleSign Changes of E(T), Δ(x), and P(x)en_US
dc.typeArticleen_US
dc.identifier.emailTsang, K:kmtsang@maths.hku.hken_US
dc.identifier.authorityTsang, K=rp00793en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1006/jnth.1994.1081en_US
dc.identifier.scopuseid_2-s2.0-0010425508en_US
dc.identifier.hkuros36032-
dc.identifier.volume49en_US
dc.identifier.issue1en_US
dc.identifier.spage73en_US
dc.identifier.epage83en_US
dc.identifier.isiWOS:A1994PL38500005-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridHeathbrown, DR=24294023000en_US
dc.identifier.scopusauthoridTsang, K=7201554731en_US

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