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Article: Sign changes of error terms related to the Euler function

TitleSign changes of error terms related to the Euler function
Authors
KeywordsSign Changes
Error Terms
Euler Function
Issue Date1999
PublisherLondon Mathematical Society. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=MTK
Citation
Mathematika, 1999, v. 46 n. 2, p. 391-395 How to Cite?
AbstractLet φ(n) be the Euler function (i.e., φ(n) denotes the number of integers less than n which are relatively prime to n), and define R(x)= ∑n<=x φ(n)- 3/π2 x2, H(x)= ∑n<=x φ(n)/n - 6/π2 x. These functions were extensively studied by several mathematicians. One of the problems investigated concerns their sign changes. We say that a function fx) has a sign change at x = x0 if f(x0 −) f(x0 +) < 0, and f(x) has a sign change on the integer n if (n)f(n+1) < 0. The numbers of sign changes and sign changes on integers of f(x) in the interval [1, T] are denoted by Xf(T) and Nf(T), respectively.
Persistent Identifierhttp://hdl.handle.net/10722/156095
ISSN
2015 Impact Factor: 0.714
2015 SCImago Journal Rankings: 0.686
References

 

DC FieldValueLanguage
dc.contributor.authorLau, YKen_US
dc.date.accessioned2012-08-08T08:40:23Z-
dc.date.available2012-08-08T08:40:23Z-
dc.date.issued1999en_US
dc.identifier.citationMathematika, 1999, v. 46 n. 2, p. 391-395en_US
dc.identifier.issn0025-5793en_US
dc.identifier.urihttp://hdl.handle.net/10722/156095-
dc.description.abstractLet φ(n) be the Euler function (i.e., φ(n) denotes the number of integers less than n which are relatively prime to n), and define R(x)= ∑n<=x φ(n)- 3/π2 x2, H(x)= ∑n<=x φ(n)/n - 6/π2 x. These functions were extensively studied by several mathematicians. One of the problems investigated concerns their sign changes. We say that a function fx) has a sign change at x = x0 if f(x0 −) f(x0 +) < 0, and f(x) has a sign change on the integer n if (n)f(n+1) < 0. The numbers of sign changes and sign changes on integers of f(x) in the interval [1, T] are denoted by Xf(T) and Nf(T), respectively.-
dc.languageengen_US
dc.publisherLondon Mathematical Society. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=MTKen_US
dc.relation.ispartofMathematikaen_US
dc.subjectSign Changes-
dc.subjectError Terms-
dc.subjectEuler Function-
dc.titleSign changes of error terms related to the Euler functionen_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.doi10.1112/S0025579300007841-
dc.identifier.scopuseid_2-s2.0-0038853244en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0038853244&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume46en_US
dc.identifier.issue2en_US
dc.identifier.spage391en_US
dc.identifier.epage395en_US
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridLau, YK=35724053400en_US

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