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- Publisher Website: 10.1112/S0024609300007505
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Article: Counting lattice points in the sphere
| Title | Counting lattice points in the sphere |
|---|---|
| Authors | |
| Issue Date | 2000 |
| Citation | Bulletin Of The London Mathematical Society, 2000, v. 32 n. 6, p. 679-688 How to Cite? |
| Abstract | We consider the error term P3(R) = #{n ∈ ℤ3 : |n| ≤ R} - 4/3πR3 which occurs in the counting of lattice points in a sphere of radius R. By considering second and third power moments, we prove that P3(R) = Ω±(R√logR). An upper bound for the gap between the sign changes of P3(R) is also proved. |
| Persistent Identifier | http://hdl.handle.net/10722/75461 |
| ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 1.043 |
| ISI Accession Number ID | |
| References |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Tsang, KM | en_HK |
| dc.date.accessioned | 2010-09-06T07:11:20Z | - |
| dc.date.available | 2010-09-06T07:11:20Z | - |
| dc.date.issued | 2000 | en_HK |
| dc.identifier.citation | Bulletin Of The London Mathematical Society, 2000, v. 32 n. 6, p. 679-688 | en_HK |
| dc.identifier.issn | 0024-6093 | en_HK |
| dc.identifier.uri | http://hdl.handle.net/10722/75461 | - |
| dc.description.abstract | We consider the error term P3(R) = #{n ∈ ℤ3 : |n| ≤ R} - 4/3πR3 which occurs in the counting of lattice points in a sphere of radius R. By considering second and third power moments, we prove that P3(R) = Ω±(R√logR). An upper bound for the gap between the sign changes of P3(R) is also proved. | en_HK |
| dc.language | eng | en_HK |
| dc.relation.ispartof | Bulletin of the London Mathematical Society | en_HK |
| dc.title | Counting lattice points in the sphere | en_HK |
| dc.type | Article | 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 | 10.1112/S0024609300007505 | - |
| dc.identifier.scopus | eid_2-s2.0-0038831427 | en_HK |
| dc.identifier.hkuros | 63187 | en_HK |
| dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0038831427&selection=ref&src=s&origin=recordpage | en_HK |
| dc.identifier.volume | 32 | en_HK |
| dc.identifier.issue | 6 | en_HK |
| dc.identifier.spage | 679 | en_HK |
| dc.identifier.epage | 688 | en_HK |
| dc.identifier.isi | WOS:000165978200007 | - |
| dc.publisher.place | United Kingdom | en_HK |
| dc.identifier.scopusauthorid | Tsang, KM=7201554731 | en_HK |
| dc.identifier.issnl | 0024-6093 | - |