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Article: On almost prime k-tuples

TitleOn almost prime k-tuples
Authors
KeywordsPrime k-tuples
Primes
Sieves
Issue Date2006
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt
Citation
Journal Of Number Theory, 2006, v. 120 n. 1, p. 33-46 How to Cite?
AbstractLet k ≥ 2 and ai, bi(1 ≤ i ≤ k) be integers such that ai > 0 and ∏1 ≤ i < j ≤ k (ai bj - aj bi) ≠ 0. Let Ω (m) denote the total number of prime factors of m. Suppose ∏ (n) : = ∏i = 1 k (ai n + bi) has no fixed prime divisors. Results of the form # {n ≤ x : Ω (∏ (n)) ≤ rk} ≫ x (log x)- k where rk is asymptotic to k log k have been obtained by using sieve methods, in particular weighted sieves. In this paper, we use another kind of weighted sieve due to Selberg to obtain improved admissible values for rk. © 2005 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75248
ISSN
2015 Impact Factor: 0.596
2015 SCImago Journal Rankings: 0.858
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorHo, KHen_HK
dc.contributor.authorTsang, KMen_HK
dc.date.accessioned2010-09-06T07:09:20Z-
dc.date.available2010-09-06T07:09:20Z-
dc.date.issued2006en_HK
dc.identifier.citationJournal Of Number Theory, 2006, v. 120 n. 1, p. 33-46en_HK
dc.identifier.issn0022-314Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/75248-
dc.description.abstractLet k ≥ 2 and ai, bi(1 ≤ i ≤ k) be integers such that ai > 0 and ∏1 ≤ i < j ≤ k (ai bj - aj bi) ≠ 0. Let Ω (m) denote the total number of prime factors of m. Suppose ∏ (n) : = ∏i = 1 k (ai n + bi) has no fixed prime divisors. Results of the form # {n ≤ x : Ω (∏ (n)) ≤ rk} ≫ x (log x)- k where rk is asymptotic to k log k have been obtained by using sieve methods, in particular weighted sieves. In this paper, we use another kind of weighted sieve due to Selberg to obtain improved admissible values for rk. © 2005 Elsevier Inc. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnten_HK
dc.relation.ispartofJournal of Number Theoryen_HK
dc.subjectPrime k-tuplesen_HK
dc.subjectPrimesen_HK
dc.subjectSievesen_HK
dc.titleOn almost prime k-tuplesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0022-314X&volume=120&spage=33&epage=46&date=2006&atitle=On+almost+prime+k-tuplesen_HK
dc.identifier.emailTsang, KM:kmtsang@maths.hku.hken_HK
dc.identifier.authorityTsang, KM=rp00793en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jnt.2005.11.014en_HK
dc.identifier.scopuseid_2-s2.0-33746793220en_HK
dc.identifier.hkuros122421en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33746793220&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume120en_HK
dc.identifier.issue1en_HK
dc.identifier.spage33en_HK
dc.identifier.epage46en_HK
dc.identifier.eissn1096-1658-
dc.identifier.isiWOS:000240526600004-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridHo, KH=14057863700en_HK
dc.identifier.scopusauthoridTsang, KM=7201554731en_HK

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