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Article: Omega result for the mean square of the Riemann zeta function

TitleOmega result for the mean square of the Riemann zeta function
Authors
Lau, YKTsang, KM
Issue Date2005
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00229/index.htm
Citation
Manuscripta Mathematica, 2005, v. 117 n. 3, p. 373-381 How to Cite?
DOI: http://dx.doi.org/10.1007/s00229-005-0565-2
AbstractA recent method of Soundararajan enables one to obtain improved Ω-result for finite series of the form Σn f(n) cos (2π λ n x+β) where 0<λ 1<λ 2<. . . and β are real numbers and the coefficients f(n) are all non-negative. In this paper, Soundararajan's method is adapted to obtain improved Ω-result for E(t), the remainder term in the mean-square formula for the Riemann zeta-function on the critical line. The Atkinson series for E(t) is of the above type, but with an oscillating factor (-1) n attached to each of its terms. © Springer-Verlag 2005.
Persistent Identifierhttp://hdl.handle.net/10722/75179
ISSN
0025-2611
2021 Impact Factor: 0.640
2020 SCImago Journal Rankings: 0.752
ISI Accession Number ID
WOS:000230462300009
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorLau, YKen_HK
dc.contributor.authorTsang, KMen_HK
dc.date.accessioned2010-09-06T07:08:42Z-
dc.date.available2010-09-06T07:08:42Z-
dc.date.issued2005en_HK
dc.identifier.citationManuscripta Mathematica, 2005, v. 117 n. 3, p. 373-381en_HK
dc.identifier.issn0025-2611en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75179-
dc.description.abstractA recent method of Soundararajan enables one to obtain improved Ω-result for finite series of the form Σn f(n) cos (2π λ n x+β) where 0<λ 1<λ 2<. . . and β are real numbers and the coefficients f(n) are all non-negative. In this paper, Soundararajan's method is adapted to obtain improved Ω-result for E(t), the remainder term in the mean-square formula for the Riemann zeta-function on the critical line. The Atkinson series for E(t) is of the above type, but with an oscillating factor (-1) n attached to each of its terms. © Springer-Verlag 2005.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00229/index.htmen_HK
dc.relation.ispartofManuscripta Mathematicaen_HK
dc.titleOmega result for the mean square of the Riemann zeta functionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0025-2611&volume=117&spage=373&epage=381&date=2005&atitle=Omega+result+for+the+mean+square+of+the+Riemann+zeta+functionen_HK
dc.identifier.emailLau, YK:yklau@maths.hku.hken_HK
dc.identifier.emailTsang, KM:kmtsang@maths.hku.hken_HK
dc.identifier.authorityLau, YK=rp00722en_HK
dc.identifier.authorityTsang, KM=rp00793en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s00229-005-0565-2en_HK
dc.identifier.scopuseid_2-s2.0-22544435236en_HK
dc.identifier.hkuros112472en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-22544435236&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume117en_HK
dc.identifier.issue3en_HK
dc.identifier.spage373en_HK
dc.identifier.epage381en_HK
dc.identifier.isiWOS:000230462300009-
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridLau, YK=35724053400en_HK
dc.identifier.scopusauthoridTsang, KM=7201554731en_HK
dc.identifier.issnl0025-2611-

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