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Article: Higher-power moments of δ(x), E(t) and P(x)

TitleHigher-power moments of δ(x), E(t) and P(x)
Authors
Issue Date1992
PublisherOxford University Press. The Journal's web site is located at http://plms.oxfordjournals.org/
Citation
Proceedings of the London Mathematical Society, 1992, v. s3-65 n. 1, p. 65-84 How to Cite?
AbstractLet δ(x denote the error term in the asymptotic formula for the divisor sum. Using a Voronoi-type formula for δ(x, we prove that \int_{x}^{2} △(x)^3dx≈cX^{7/4} and \int_{x}^{2} △(x)^4dx≈c’X^2, where c and c′ are some positive constants. The estimate for the third-power moment shows that δ3(x) is strongly biased towards the positive side. We also obtain similar results for E(t), the error term in the mean square formula for the Riemann zeta-function on the critical line, and for P(x), the error term in the circle problem.
Persistent Identifierhttp://hdl.handle.net/10722/75307
ISSN
2015 Impact Factor: 1.079
2015 SCImago Journal Rankings: 2.416

 

DC FieldValueLanguage
dc.contributor.authorTsang, KMen_HK
dc.date.accessioned2010-09-06T07:09:53Z-
dc.date.available2010-09-06T07:09:53Z-
dc.date.issued1992en_HK
dc.identifier.citationProceedings of the London Mathematical Society, 1992, v. s3-65 n. 1, p. 65-84en_HK
dc.identifier.issn0024-6115-
dc.identifier.urihttp://hdl.handle.net/10722/75307-
dc.description.abstractLet δ(x denote the error term in the asymptotic formula for the divisor sum. Using a Voronoi-type formula for δ(x, we prove that \int_{x}^{2} △(x)^3dx≈cX^{7/4} and \int_{x}^{2} △(x)^4dx≈c’X^2, where c and c′ are some positive constants. The estimate for the third-power moment shows that δ3(x) is strongly biased towards the positive side. We also obtain similar results for E(t), the error term in the mean square formula for the Riemann zeta-function on the critical line, and for P(x), the error term in the circle problem.-
dc.languageengen_HK
dc.publisherOxford University Press. The Journal's web site is located at http://plms.oxfordjournals.org/-
dc.relation.ispartofProceedings of the London Mathematical Societyen_HK
dc.titleHigher-power moments of δ(x), E(t) and P(x)en_HK
dc.typeArticleen_HK
dc.identifier.emailTsang, KM: kmtsang@maths.hku.hken_HK
dc.identifier.authorityTsang, KM=rp00793en_HK
dc.identifier.doi10.1112/plms/s3-65.1.65-
dc.identifier.hkuros36028en_HK
dc.identifier.volumes3-65-
dc.identifier.issue1-
dc.identifier.spage65-
dc.identifier.epage84-
dc.publisher.placeUnited Kingdom-

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