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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. 391395 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  2015 Impact Factor: 0.714 2015 SCImago Journal Rankings: 0.686 
References 
DC Field  Value  Language 

dc.contributor.author  Lau, YK  en_US 
dc.date.accessioned  20120808T08:40:23Z   
dc.date.available  20120808T08:40:23Z   
dc.date.issued  1999  en_US 
dc.identifier.citation  Mathematika, 1999, v. 46 n. 2, p. 391395  en_US 
dc.identifier.issn  00255793  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_2s2.00038853244  en_US 
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.00038853244&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.publisher.place  United Kingdom  en_US 
dc.identifier.scopusauthorid  Lau, YK=35724053400  en_US 