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Article: On a weighted mean square result of the error terms of some arithmetical functions

TitleOn a weighted mean square result of the error terms of some arithmetical functions
Authors
KeywordsArithmetical Functions
Dirichlet Series
Mean Square Formula
Issue Date2000
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt
Citation
Journal Of Number Theory, 2000, v. 80 n. 1, p. 89-108 How to Cite?
AbstractLet a(n) be an arithmetical function satisfying some conditions and write ∑′n≤xa(n)=main term+E(x). We obtain an asymptotic formula for a weighted mean square of the error term∫1T|E(y)|2y2σ 0 +1dy∼clogT for some constants σ0 and c, by modifying a method that seems due to Titchmarsh. This method utilizes the following tools: the Perron formula, the Parseval Theorem, and a Tauberian Theorem. The main difference between the present and the original method is that we include the contribution of the poles of the associated Dirichlet series on a certain line in the main term. © 2000 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/156081
ISSN
2015 Impact Factor: 0.596
2015 SCImago Journal Rankings: 0.858
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLau, YKen_US
dc.date.accessioned2012-08-08T08:40:19Z-
dc.date.available2012-08-08T08:40:19Z-
dc.date.issued2000en_US
dc.identifier.citationJournal Of Number Theory, 2000, v. 80 n. 1, p. 89-108en_US
dc.identifier.issn0022-314Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/156081-
dc.description.abstractLet a(n) be an arithmetical function satisfying some conditions and write ∑′n≤xa(n)=main term+E(x). We obtain an asymptotic formula for a weighted mean square of the error term∫1T|E(y)|2y2σ 0 +1dy∼clogT for some constants σ0 and c, by modifying a method that seems due to Titchmarsh. This method utilizes the following tools: the Perron formula, the Parseval Theorem, and a Tauberian Theorem. The main difference between the present and the original method is that we include the contribution of the poles of the associated Dirichlet series on a certain line in the main term. © 2000 Academic Press.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.subjectArithmetical Functionsen_US
dc.subjectDirichlet Seriesen_US
dc.subjectMean Square Formulaen_US
dc.titleOn a weighted mean square result of the error terms of some arithmetical functionsen_US
dc.typeArticleen_US
dc.identifier.emailLau, YK:yklau@maths.hku.hken_US
dc.identifier.authorityLau, YK=rp00722en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1006/jnth.1999.2436-
dc.identifier.scopuseid_2-s2.0-0033634569en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0033634569&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume80en_US
dc.identifier.issue1en_US
dc.identifier.spage89en_US
dc.identifier.epage108en_US
dc.identifier.isiWOS:000084882400005-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLau, YK=35724053400en_US

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