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Article: Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function
Title | Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function |
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Authors | |
Keywords | divisor problems mean values Riemann's zeta-function |
Issue Date | 2010 |
Publisher | Science 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? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/129254 |
ISSN | 2023 Impact Factor: 1.4 2023 SCImago Journal Rankings: 1.060 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Tsang, KM | en_HK |
dc.date.accessioned | 2010-12-23T08:34:14Z | - |
dc.date.available | 2010-12-23T08:34:14Z | - |
dc.date.issued | 2010 | en_HK |
dc.identifier.citation | Science China Mathematics, 2010, v. 53 n. 9, p. 2561-2572 | en_HK |
dc.identifier.issn | 1674-7283 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/129254 | - |
dc.description.abstract | Let 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.language | eng | en_US |
dc.publisher | Science China Press, co-published with Springer. The Journal's web site is located at http://math.scichina.com/english/ | en_HK |
dc.relation.ispartof | Science China Mathematics | en_HK |
dc.subject | divisor problems | en_HK |
dc.subject | mean values | en_HK |
dc.subject | Riemann's zeta-function | en_HK |
dc.title | Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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.email | Tsang, KM:kmtsang@maths.hku.hk | en_HK |
dc.identifier.authority | Tsang, KM=rp00793 | en_HK |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1007/s11425-010-4068-6 | en_HK |
dc.identifier.scopus | eid_2-s2.0-77956480009 | en_HK |
dc.identifier.hkuros | 183322 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-77956480009&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 53 | en_HK |
dc.identifier.issue | 9 | en_HK |
dc.identifier.spage | 2561 | en_HK |
dc.identifier.epage | 2572 | en_HK |
dc.identifier.eissn | 1869-1862 | - |
dc.identifier.isi | WOS:000281670200030 | - |
dc.publisher.place | China | en_HK |
dc.identifier.scopusauthorid | Tsang, KM=7201554731 | en_HK |
dc.identifier.issnl | 1869-1862 | - |