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Article: Sign changes of error terms related to the Euler function
Title | Sign changes of error terms related to the Euler function |
---|---|
Authors | |
Keywords | Sign Changes Error Terms Euler Function |
Issue Date | 1999 |
Publisher | London 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? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/156095 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 0.847 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Lau, YK | en_US |
dc.date.accessioned | 2012-08-08T08:40:23Z | - |
dc.date.available | 2012-08-08T08:40:23Z | - |
dc.date.issued | 1999 | en_US |
dc.identifier.citation | Mathematika, 1999, v. 46 n. 2, p. 391-395 | en_US |
dc.identifier.issn | 0025-5793 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156095 | - |
dc.description.abstract | Let 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.language | eng | en_US |
dc.publisher | London Mathematical Society. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=MTK | en_US |
dc.relation.ispartof | Mathematika | en_US |
dc.subject | Sign Changes | - |
dc.subject | Error Terms | - |
dc.subject | Euler Function | - |
dc.title | Sign changes of error terms related to the Euler function | en_US |
dc.type | Article | en_US |
dc.identifier.email | Lau, YK:yklau@maths.hku.hk | en_US |
dc.identifier.authority | Lau, YK=rp00722 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1112/S0025579300007841 | - |
dc.identifier.scopus | eid_2-s2.0-0038853244 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0038853244&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 46 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 391 | en_US |
dc.identifier.epage | 395 | en_US |
dc.identifier.isi | WOS:000169042300012 | - |
dc.publisher.place | United Kingdom | en_US |
dc.identifier.scopusauthorid | Lau, YK=35724053400 | en_US |
dc.identifier.issnl | 0025-5793 | - |