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- Publisher Website: 10.1006/jnth.1994.1081
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Article: Sign Changes of E(T), Δ(x), and P(x)
| Title | Sign Changes of E(T), Δ(x), and P(x) |
|---|---|
| Authors | |
| Issue Date | 1994 |
| Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt |
| Citation | Journal Of Number Theory, 1994, v. 49 n. 1, p. 73-83 How to Cite? |
| Abstract | Let Δ(x), P(x), and E(T) denote the usual error terms in the divisor problem, the circle problem, and the mean value theorem for |ζ( 1 2 + it)| 2. It is not hard to prove that, for a suitable constant C, each of these error terms changes sign on every interval [K, K + C √K]. We show, in contrast, that a positive proportion of intervals [K, K + C √K (log K) -5] contain no such sign change. In the case of E(T) this disproves a conjecture of A. Ivić and H. J. J. te Riele (Math. Comp.56, 1991, 303-328). © 1994 Academic Press. All rights reserved. |
| Persistent Identifier | http://hdl.handle.net/10722/156047 |
| ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 0.780 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Heathbrown, DR | en_US |
| dc.contributor.author | Tsang, K | en_US |
| dc.date.accessioned | 2012-08-08T08:40:11Z | - |
| dc.date.available | 2012-08-08T08:40:11Z | - |
| dc.date.issued | 1994 | en_US |
| dc.identifier.citation | Journal Of Number Theory, 1994, v. 49 n. 1, p. 73-83 | en_US |
| dc.identifier.issn | 0022-314X | en_US |
| dc.identifier.uri | http://hdl.handle.net/10722/156047 | - |
| dc.description.abstract | Let Δ(x), P(x), and E(T) denote the usual error terms in the divisor problem, the circle problem, and the mean value theorem for |ζ( 1 2 + it)| 2. It is not hard to prove that, for a suitable constant C, each of these error terms changes sign on every interval [K, K + C √K]. We show, in contrast, that a positive proportion of intervals [K, K + C √K (log K) -5] contain no such sign change. In the case of E(T) this disproves a conjecture of A. Ivić and H. J. J. te Riele (Math. Comp.56, 1991, 303-328). © 1994 Academic Press. All rights reserved. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt | en_US |
| dc.relation.ispartof | Journal of Number Theory | en_US |
| dc.title | Sign Changes of E(T), Δ(x), and P(x) | en_US |
| dc.type | Article | en_US |
| dc.identifier.email | Tsang, K:kmtsang@maths.hku.hk | en_US |
| dc.identifier.authority | Tsang, K=rp00793 | en_US |
| dc.description.nature | link_to_subscribed_fulltext | en_US |
| dc.identifier.doi | 10.1006/jnth.1994.1081 | en_US |
| dc.identifier.scopus | eid_2-s2.0-0010425508 | en_US |
| dc.identifier.hkuros | 36032 | - |
| dc.identifier.volume | 49 | en_US |
| dc.identifier.issue | 1 | en_US |
| dc.identifier.spage | 73 | en_US |
| dc.identifier.epage | 83 | en_US |
| dc.identifier.isi | WOS:A1994PL38500005 | - |
| dc.publisher.place | United States | en_US |
| dc.identifier.scopusauthorid | Heathbrown, DR=24294023000 | en_US |
| dc.identifier.scopusauthorid | Tsang, K=7201554731 | en_US |
| dc.identifier.issnl | 0022-314X | - |