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Article: On Lagrange's four squares theorem with almost prime variables
Title | On Lagrange's four squares theorem with almost prime variables |
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Authors | |
Issue Date | 2017 |
Publisher | Walter de Gruyter GmbH & Co KG. The Journal's web site is located at http://www.degruyter.com/view/j/crll?rskey=R7TouQ&result=189&q= |
Citation | Journal fur die Reine und Angewandte Mathematik, 2017, v. 2017 n. 726, p. 129-171 How to Cite? |
Abstract | In 1994, Brüdern and Fouvry [1] initiated the investigation of Lagrange’s four squares theorem with almost prime variables. In this paper, we prove that every sufficiently large integer, congruent to 4 modulo 24, can be represented as a sum of four squares of integers, each of which has at most four prime factors. Instead of the four-dimensional vector sieve developed by Brüdern and Fouvry [1], we establish this result by combining the three-dimensional sieve and the switching principle. |
Persistent Identifier | http://hdl.handle.net/10722/245057 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 1.894 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Tsang, KM | - |
dc.contributor.author | Zhao, L | - |
dc.date.accessioned | 2017-09-18T02:03:52Z | - |
dc.date.available | 2017-09-18T02:03:52Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Journal fur die Reine und Angewandte Mathematik, 2017, v. 2017 n. 726, p. 129-171 | - |
dc.identifier.issn | 0075-4102 | - |
dc.identifier.uri | http://hdl.handle.net/10722/245057 | - |
dc.description.abstract | In 1994, Brüdern and Fouvry [1] initiated the investigation of Lagrange’s four squares theorem with almost prime variables. In this paper, we prove that every sufficiently large integer, congruent to 4 modulo 24, can be represented as a sum of four squares of integers, each of which has at most four prime factors. Instead of the four-dimensional vector sieve developed by Brüdern and Fouvry [1], we establish this result by combining the three-dimensional sieve and the switching principle. | - |
dc.language | eng | - |
dc.publisher | Walter de Gruyter GmbH & Co KG. The Journal's web site is located at http://www.degruyter.com/view/j/crll?rskey=R7TouQ&result=189&q= | - |
dc.relation.ispartof | Journal fur die Reine und Angewandte Mathematik | - |
dc.rights | © De Gruyter 2017. The final publication is available at www.degruyter.com | - |
dc.title | On Lagrange's four squares theorem with almost prime variables | - |
dc.type | Article | - |
dc.identifier.email | Tsang, KM: kmtsang@hkucc.hku.hk | - |
dc.identifier.authority | Tsang, KM=rp00793 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1515/crelle-2014-0094 | - |
dc.identifier.scopus | eid_2-s2.0-85019208620 | - |
dc.identifier.hkuros | 278420 | - |
dc.identifier.volume | 2017 | - |
dc.identifier.issue | 726 | - |
dc.identifier.spage | 129 | - |
dc.identifier.epage | 171 | - |
dc.identifier.isi | WOS:000400160400005 | - |
dc.publisher.place | Germany | - |
dc.identifier.issnl | 0075-4102 | - |