File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Conditional bounds for small prime solutions of linear equations

TitleConditional bounds for small prime solutions of linear equations
Authors
Issue Date1992
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00229/index.htm
Citation
Manuscripta Mathematica, 1992, v. 74 n. 1, p. 321-340 How to Cite?
AbstractLet a 1, a 2, a 3 be non-zero integers with gcd(a 1 a 2, a 3)=1 and let b be an arbitrary integer satisfying gcd (b, a i, a j) =1 for i≠j and b≡a 1+a 2+a 3 (mod 2). In a previous paper [3] which completely settled a problem of A. Baker, the 2nd and 3rd authors proved that if a 1, a 2, a 3 are not all of the same sign, then the equation a 1 p 1+a 2 p 2+a 3 p 3=b has a solution in primes p j satisfying {Mathematical expression} where A>0 is an absolute constant. In this paper, under the Generalized Riemann Hypothesis, the authors obtain a more precise bound for the solutions p j . In particular they obtain A<4+∈ for some ∈>0. An immediate consquence of the main result is that the Linnik's courtant is less than or equal to 2. © 1992 Springer-Verlag.
Persistent Identifierhttp://hdl.handle.net/10722/75342
ISSN
2015 Impact Factor: 0.591
2015 SCImago Journal Rankings: 0.967
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChoi, KKen_HK
dc.contributor.authorLiu, MCen_HK
dc.contributor.authorTsang, KMen_HK
dc.date.accessioned2010-09-06T07:10:13Z-
dc.date.available2010-09-06T07:10:13Z-
dc.date.issued1992en_HK
dc.identifier.citationManuscripta Mathematica, 1992, v. 74 n. 1, p. 321-340en_HK
dc.identifier.issn0025-2611en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75342-
dc.description.abstractLet a 1, a 2, a 3 be non-zero integers with gcd(a 1 a 2, a 3)=1 and let b be an arbitrary integer satisfying gcd (b, a i, a j) =1 for i≠j and b≡a 1+a 2+a 3 (mod 2). In a previous paper [3] which completely settled a problem of A. Baker, the 2nd and 3rd authors proved that if a 1, a 2, a 3 are not all of the same sign, then the equation a 1 p 1+a 2 p 2+a 3 p 3=b has a solution in primes p j satisfying {Mathematical expression} where A>0 is an absolute constant. In this paper, under the Generalized Riemann Hypothesis, the authors obtain a more precise bound for the solutions p j . In particular they obtain A<4+∈ for some ∈>0. An immediate consquence of the main result is that the Linnik's courtant is less than or equal to 2. © 1992 Springer-Verlag.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00229/index.htmen_HK
dc.relation.ispartofManuscripta Mathematicaen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleConditional bounds for small prime solutions of linear equationsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0025-2611&volume=74&spage=321&epage=340&date=1992&atitle=Conditional+bounds+for+small+prime+solutions+of+linear+equationsen_HK
dc.identifier.emailTsang, KM:kmtsang@maths.hku.hken_HK
dc.identifier.authorityTsang, KM=rp00793en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1007/BF02567674en_HK
dc.identifier.scopuseid_2-s2.0-51249166825en_HK
dc.identifier.hkuros34788en_HK
dc.identifier.volume74en_HK
dc.identifier.issue1en_HK
dc.identifier.spage321en_HK
dc.identifier.epage340en_HK
dc.identifier.isiWOS:A1992HG43300006-
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridChoi, KK=7403949729en_HK
dc.identifier.scopusauthoridLiu, MC=7406300336en_HK
dc.identifier.scopusauthoridTsang, KM=7201554731en_HK

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats