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Article: Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function

TitleRecent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function
Authors
Tsang, KM
Keywordsdivisor problems
mean values
Riemann's zeta-function
Issue Date2010
PublisherScience China Press, co-published with Springer. The Journal's web site is located at http://math.scichina.com/english/
Citation
Science China Mathematics, 2010, v. 53 n. 9, p. 2561-2572 How to Cite?
DOI: http://dx.doi.org/10.1007/s11425-010-4068-6
AbstractLet Δ(x) and E(t) denote respectively the remainder terms in the Dirichlet divisor problem and the mean square formula for the Riemann zeta-function on the critical line. This article is a survey of recent developments on the research of these famous error terms in number theory. These include upper bounds, Ω-results, sign changes, moments and distribution, etc. A few open problems are also discussed. © 2010 Science China Press and Springer-Verlag Berlin Heidelberg.
Persistent Identifierhttp://hdl.handle.net/10722/129254
ISSN
1674-7283
2023 Impact Factor: 1.4
2023 SCImago Journal Rankings: 1.060
ISI Accession Number ID
WOS:000281670200030
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorTsang, KMen_HK
dc.date.accessioned2010-12-23T08:34:14Z-
dc.date.available2010-12-23T08:34:14Z-
dc.date.issued2010en_HK
dc.identifier.citationScience China Mathematics, 2010, v. 53 n. 9, p. 2561-2572en_HK
dc.identifier.issn1674-7283en_HK
dc.identifier.urihttp://hdl.handle.net/10722/129254-
dc.description.abstractLet Δ(x) and E(t) denote respectively the remainder terms in the Dirichlet divisor problem and the mean square formula for the Riemann zeta-function on the critical line. This article is a survey of recent developments on the research of these famous error terms in number theory. These include upper bounds, Ω-results, sign changes, moments and distribution, etc. A few open problems are also discussed. © 2010 Science China Press and Springer-Verlag Berlin Heidelberg.en_HK
dc.languageengen_US
dc.publisherScience China Press, co-published with Springer. The Journal's web site is located at http://math.scichina.com/english/en_HK
dc.relation.ispartofScience China Mathematicsen_HK
dc.subjectdivisor problemsen_HK
dc.subjectmean valuesen_HK
dc.subjectRiemann's zeta-functionen_HK
dc.titleRecent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-functionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1674-7283&volume=53&issue=9&spage=2561&epage=2572&date=2010&atitle=Recent+progress+on+the+Dirichlet+divisor+problem+and+the+mean+square+of+the+Riemann+zeta-function-
dc.identifier.emailTsang, KM:kmtsang@maths.hku.hken_HK
dc.identifier.authorityTsang, KM=rp00793en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1007/s11425-010-4068-6en_HK
dc.identifier.scopuseid_2-s2.0-77956480009en_HK
dc.identifier.hkuros183322en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77956480009&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume53en_HK
dc.identifier.issue9en_HK
dc.identifier.spage2561en_HK
dc.identifier.epage2572en_HK
dc.identifier.eissn1869-1862-
dc.identifier.isiWOS:000281670200030-
dc.publisher.placeChinaen_HK
dc.identifier.scopusauthoridTsang, KM=7201554731en_HK
dc.identifier.issnl1869-1862-

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