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Article: Conditional bounds for small prime solutions of linear equations
Title | Conditional bounds for small prime solutions of linear equations |
---|---|
Authors | |
Issue Date | 1992 |
Publisher | Springer 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? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/75342 |
ISSN | 2015 Impact Factor: 0.591 2015 SCImago Journal Rankings: 0.967 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choi, KK | en_HK |
dc.contributor.author | Liu, MC | en_HK |
dc.contributor.author | Tsang, KM | en_HK |
dc.date.accessioned | 2010-09-06T07:10:13Z | - |
dc.date.available | 2010-09-06T07:10:13Z | - |
dc.date.issued | 1992 | en_HK |
dc.identifier.citation | Manuscripta Mathematica, 1992, v. 74 n. 1, p. 321-340 | en_HK |
dc.identifier.issn | 0025-2611 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75342 | - |
dc.description.abstract | Let 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.language | eng | en_HK |
dc.publisher | Springer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00229/index.htm | en_HK |
dc.relation.ispartof | Manuscripta Mathematica | en_HK |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | Conditional bounds for small prime solutions of linear equations | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+equations | en_HK |
dc.identifier.email | Tsang, KM:kmtsang@maths.hku.hk | en_HK |
dc.identifier.authority | Tsang, KM=rp00793 | en_HK |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1007/BF02567674 | en_HK |
dc.identifier.scopus | eid_2-s2.0-51249166825 | en_HK |
dc.identifier.hkuros | 34788 | en_HK |
dc.identifier.volume | 74 | en_HK |
dc.identifier.issue | 1 | en_HK |
dc.identifier.spage | 321 | en_HK |
dc.identifier.epage | 340 | en_HK |
dc.identifier.isi | WOS:A1992HG43300006 | - |
dc.publisher.place | Germany | en_HK |
dc.identifier.scopusauthorid | Choi, KK=7403949729 | en_HK |
dc.identifier.scopusauthorid | Liu, MC=7406300336 | en_HK |
dc.identifier.scopusauthorid | Tsang, KM=7201554731 | en_HK |