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Article: On almost prime k-tuples
| Title | On almost prime k-tuples |
|---|---|
| Authors | |
| Keywords | Prime k-tuples Primes Sieves |
| Issue Date | 2006 |
| Publisher | Academic 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? |
| Abstract | Let 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 Identifier | http://hdl.handle.net/10722/75248 |
| ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 0.780 |
| ISI Accession Number ID | |
| References |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Ho, KH | en_HK |
| dc.contributor.author | Tsang, KM | en_HK |
| dc.date.accessioned | 2010-09-06T07:09:20Z | - |
| dc.date.available | 2010-09-06T07:09:20Z | - |
| dc.date.issued | 2006 | en_HK |
| dc.identifier.citation | Journal Of Number Theory, 2006, v. 120 n. 1, p. 33-46 | en_HK |
| dc.identifier.issn | 0022-314X | en_HK |
| dc.identifier.uri | http://hdl.handle.net/10722/75248 | - |
| dc.description.abstract | Let 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.language | eng | en_HK |
| dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt | en_HK |
| dc.relation.ispartof | Journal of Number Theory | en_HK |
| dc.subject | Prime k-tuples | en_HK |
| dc.subject | Primes | en_HK |
| dc.subject | Sieves | en_HK |
| dc.title | On almost prime k-tuples | en_HK |
| dc.type | Article | en_HK |
| dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0022-314X&volume=120&spage=33&epage=46&date=2006&atitle=On+almost+prime+k-tuples | en_HK |
| dc.identifier.email | Tsang, KM:kmtsang@maths.hku.hk | en_HK |
| dc.identifier.authority | Tsang, KM=rp00793 | en_HK |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1016/j.jnt.2005.11.014 | en_HK |
| dc.identifier.scopus | eid_2-s2.0-33746793220 | en_HK |
| dc.identifier.hkuros | 122421 | en_HK |
| dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-33746793220&selection=ref&src=s&origin=recordpage | en_HK |
| dc.identifier.volume | 120 | en_HK |
| dc.identifier.issue | 1 | en_HK |
| dc.identifier.spage | 33 | en_HK |
| dc.identifier.epage | 46 | en_HK |
| dc.identifier.eissn | 1096-1658 | - |
| dc.identifier.isi | WOS:000240526600004 | - |
| dc.publisher.place | United States | en_HK |
| dc.identifier.scopusauthorid | Ho, KH=14057863700 | en_HK |
| dc.identifier.scopusauthorid | Tsang, KM=7201554731 | en_HK |
| dc.identifier.issnl | 0022-314X | - |