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Article: Omega result for the mean square of the Riemann zeta function
Title | Omega result for the mean square of the Riemann zeta function |
---|---|
Authors | |
Issue Date | 2005 |
Publisher | Springer 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? |
Abstract | A 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 Identifier | http://hdl.handle.net/10722/75179 |
ISSN | 2023 Impact Factor: 0.5 2023 SCImago Journal Rankings: 0.592 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Lau, YK | en_HK |
dc.contributor.author | Tsang, KM | en_HK |
dc.date.accessioned | 2010-09-06T07:08:42Z | - |
dc.date.available | 2010-09-06T07:08:42Z | - |
dc.date.issued | 2005 | en_HK |
dc.identifier.citation | Manuscripta Mathematica, 2005, v. 117 n. 3, p. 373-381 | en_HK |
dc.identifier.issn | 0025-2611 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75179 | - |
dc.description.abstract | A 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.language | eng | en_HK |
dc.publisher | Springer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00229/index.htm | en_HK |
dc.relation.ispartof | Manuscripta Mathematica | en_HK |
dc.title | Omega result for 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=0025-2611&volume=117&spage=373&epage=381&date=2005&atitle=Omega+result+for+the+mean+square+of+the+Riemann+zeta+function | en_HK |
dc.identifier.email | Lau, YK:yklau@maths.hku.hk | en_HK |
dc.identifier.email | Tsang, KM:kmtsang@maths.hku.hk | en_HK |
dc.identifier.authority | Lau, YK=rp00722 | en_HK |
dc.identifier.authority | Tsang, KM=rp00793 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00229-005-0565-2 | en_HK |
dc.identifier.scopus | eid_2-s2.0-22544435236 | en_HK |
dc.identifier.hkuros | 112472 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-22544435236&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 117 | en_HK |
dc.identifier.issue | 3 | en_HK |
dc.identifier.spage | 373 | en_HK |
dc.identifier.epage | 381 | en_HK |
dc.identifier.isi | WOS:000230462300009 | - |
dc.publisher.place | Germany | en_HK |
dc.identifier.scopusauthorid | Lau, YK=35724053400 | en_HK |
dc.identifier.scopusauthorid | Tsang, KM=7201554731 | en_HK |
dc.identifier.issnl | 0025-2611 | - |